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Quiz about The mis adventures of Connie Conic

The (mis) adventures of Connie Conic Quiz

This quiz is all about the conic sections and their properties! Enjoy!

A multiple-choice quiz by Mrs_Seizmagraff. Estimated time: 8 mins.

Author
Mrs_Seizmagraff

Time
8 mins

Type
Multiple Choice

Quiz #
184,117

Updated
Dec 03 21

# Qns
20

Difficulty
Tough

Avg Score
11 / 20

Plays
576

One at a Time - Single Page - Timed Game

Question 1 of 20

1. Connie likes to generate conic sections. How many different (non-degenerate) ones can she generate? Hint

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Question 2 of 20

2. How does Connie generate conic sections? She intersects a plane with a ___________. (She is able to generate all of the conic sections this way) Hint

Single napped cone

Right circular cylinder

Dandelin sphere

Double napped cone

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Question 3 of 20

3. Connie likes her parabolas. Every now and then, however, she comes across a degenerate in her collection. Which of the following could NOT be a degenerate parabola? Hint

Straight line

No graph

Parallel lines

Intersecting lines

4. Connie likes to draw different shapes. One shape she gets by drawing all points that are the same distance from a fixed point as they are from a fixed line. What conic section would this shape correspond to? Hint

Circle

Hyperbola

Ellipse

Parabola

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Question 5 of 20

5. Connie often finds it hard to direct and focus her attention. If she is drawing a conic section using the "eccentricity" definition (this is the ratio of distances between a given point on the conic and a fixed point divided by the distance to a fixed line), what is the term for the fixed point?

Answer: (Read the question carefully)

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Question 6 of 20

6. Sometimes Connie likes to draw her conics a different way. One conic section can be described as the set of all points such that the sum of the distances from a given point to two fixed points is a constant. What conic section is this? Hint

Parabola

Ellipse

Hyperbola

Circle

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Question 7 of 20

7. Connie likes to star gaze; she loves Orion, the Big Dipper, and Brad Pitt. The planets orbit the sun in the shape of a conic section, which one is it?

Answer: (A conic section)

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Question 8 of 20

8. The word "ellipse" comes from the Greek word "ellipsis" which means "deficiency". Connie's cousin, Miss Polly Nomial, asked her why they would name the ellipse this way. What did Connie tell her? Hint

The eccentricity of an ellipse is always less than one, and is thus "deficient"

All other conic sections have two foci, but the ellipse only has one, so it is "deficient"

An ellipse resembles a squashed circle, so it is "deficient"

The circle has an infinite number of lines of symmetry, but the ellipse only has one; it is thus "deficient"

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Question 9 of 20

9. What could Connie point to to illustrate a degenerate circle?

Answer: (Again, read the question carefully!)

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Question 10 of 20

10. Connie knows that the conic sections are also known as "quadratic relations". Why is this? Hint

The algebraic equations of the conics are all of degree 2 (ie, quadratic)

There are 4 of them (aka, quadratic)

All of the conics can be modeled in 4 steps (hence, quadratic)

The conics can all be inscribed in a quadrilateral (thus, quadratic)

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Question 11 of 20

11. Connie's Russian cousin, Konichskaya Konnicevsky, is over for a visit. Konichskaya recounts how, during the cold war, the USSR had many satellites in orbit to spy on the US (and vice versa). Connie points out that the orbit was the shape of a conic section! What conic section would this be?

Hint

Parabola

Ellipse

Circle

Hyperbola

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Question 12 of 20

12. Someone asked Connie how to find the center of a particular conic. Connie replied, "that conic doesn't have a center". Assuming that the conic is non-degenerate, is what Connie said true? Or could she just be lying because she doesn't want to find the center of the conic? Hint

Connie is lying - all conic sections have a center

Connie is telling the truth - the conic is a parabola and they do not have a center

Connie is telling the truth - the conic is a hyperbola and they do not have a center

Connie is lying - all conics have at least one focus, and the focus is the same as the center

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Question 13 of 20

13. Connie's cousin, Miss Polly Nomial, was over for a visit, and was looking through Connie's conics collection. She recognized the parabola as a shape that she has in her polynomial functions collection. Would she recognize any of the others? Hint

Yes - the hyperbola can also be represented as a polynomial function

No - the circle, ellipse, and hyperbola are not polynomial functions

No - none of the other conic sections can ever be functions

Yes - with the right orientation, all conic sections are polynomial functions

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Question 14 of 20

14. Connie loves geometry. Who was the first geometer to write an extensive treaty on the conic sections? Hint

Archimedes of Syracuse

HSM Coxeter of the University of Toronto

Euclid of Alexandria

Appolonius of Perga

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Question 15 of 20

15. Connie finds some geometry a little "plane", but she loves projective geometry. What is the fundamental result of projective geometry for conic sections? Hint

All conic sections can be projected into each other

All lines can be projected into conic sections

All conic sections are projections of the unit sphere

All conic sections can be projected from a cone

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Question 16 of 20

16. Connie also loves inversive geometry. How are the conic sections defined in inversive geometry? "A conic section is the inverse of a ________ in a _________." Hint

line, circle

circle, circle

circle, line

line, line

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Question 17 of 20

17. Connie has graphed a conic section with the equation Ax^2+Cy^2+Dx+Ey+F=0, where A,C...F are real numbers. The graph is an ellipse, but not a circle. What do we know about the values of A and C? (Here, "AC" means the product of the numbers A and C) Hint

AC is greater than 0, A is equal to C

AC is greater than 0, A is not equal to C

AC = 0, A is not equal to C

AC is less than 0

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Question 18 of 20

18. The ellipse and the hyperbola both have a "major axis" and a "minor axis".

True

False

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Question 19 of 20

19. Connie knows that there are four types of quadratic relations. Approximately how many types of cubic relations are there? Hint

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Question 20 of 20

20. Polly asked Connie what her favourite conic section is. "Well, Polly, I love them all! But my absolute favourite is the one with the asymptotes." Which conic section is Connie's favourite? Hint

The parabola - the only one with asymptotes

The ellipse and the hyperbola - they both have asymptotes

The hyperbola - the only one with asymptotes

All of them - they all have asymptotes

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Quiz Answer Key and Fun Facts

1. Connie likes to generate conic sections. How many different (non-degenerate) ones can she generate?

Answer: 4

There are four different types of conic section: circle, ellipse, parabola, and hyperbola. The Greeks (and some mathematicians) consider the circle a special form of the ellipse, but the circle is studied as a conic section in its own right.

2. How does Connie generate conic sections? She intersects a plane with a ___________. (She is able to generate all of the conic sections this way)

Answer: Double napped cone

A single napped cone cannot generate a hyperbola (it can only do half a hyperbola), and a cylinder can only generate the ellipse and the circle. The Dandelin sphere is a device used to model the properties of the conic sections.

3. Connie likes her parabolas. Every now and then, however, she comes across a degenerate in her collection. Which of the following could NOT be a degenerate parabola?

Answer: Intersecting lines

The intersecting lines is a degenerate hyperbola.

Answer: Parabola

Conic sections can be defined based on their eccentricity, which is the ratio of distances between a point on the conic and a fixed point divided by the distance to a fixed line. If this ratio is less than one, the conic is an ellipse. If the ratio is greater than one, the conic is a hyperbola. If the ratio is exactly one (like in this case), the conic is a parabola.

Answer: Focus

The fixed point is the focus, the fixed line is called the directrix. The eccentricity ratio is often expressed e = PF/PD, where PF is the distance from a given point (P) to the focus divided by the distance to the directrix.

Answer: Ellipse

If you had an elliptical pool table and you had a ball at one focus and hit it, no matter where it hit the outside of the pool table it would always rebound in the direction of the other focus. The hyperbola can also be defined like this: it is the set of all points such that the DIFFERENCE of the distances between two fixed points is a constant.

7. Connie likes to star gaze; she loves Orion, the Big Dipper, and Brad Pitt. The planets orbit the sun in the shape of a conic section, which one is it?

Answer: Ellipse

Kepler proved his famous three laws of planetary motion in the 1500s, one of them was that the planets orbit the sun in an elliptical path.

Answer: The eccentricity of an ellipse is always less than one, and is thus "deficient"

The word "hyperbola" derives from the Greek "hyperbole" which means "excessive". The eccentricity of a hyperbola is always greater than one.

9. What could Connie point to to illustrate a degenerate circle?

Answer: Point

If a plane passes through the vertex of the double napped cone, it will produce only one point.

10. Connie knows that the conic sections are also known as "quadratic relations". Why is this?

Answer: The algebraic equations of the conics are all of degree 2 (ie, quadratic)

The general equation of degree 2 is Ax^2+Bxy+Cy^2+Dx+Ey+F=0, where A, B...F are all real numbers. The graph of this equation will ALWAYS be a conic section (or one of their degenerates).

Answer: Circle

The technical term is "geo-synchronous orbit", ie) in synchronicity with the Earth. An elliptical orbit would not be efficient as the satellite's distance to the Earth would never be constant. Parabolic and hyperbolic orbits would be useless, as the satellite would orbit once and then never come back!

Answer: Connie is telling the truth - the conic is a parabola and they do not have a center

The circle (obviously) has a center. The ellipse and the hyperbola each have 2 foci (plural of focus), and the center is the midpoint of these foci. The parabola does not have a center, since it has only one line of symmetry.

Answer: No - the circle, ellipse, and hyperbola are not polynomial functions

The circle and the ellipse can never be functions. The hyperbola CAN be a function (say y=1/x which is equivalent to xy-1=0) but not a polynomial function. Polly has her own quiz online...

14. Connie loves geometry. Who was the first geometer to write an extensive treaty on the conic sections?

Answer: Appolonius of Perga

Born about 295 BC, Appolonius published a 9-volume treatise on the conic sections, the first of its kind. It remains the definitive text on the plane subject.

15. Connie finds some geometry a little "plane", but she loves projective geometry. What is the fundamental result of projective geometry for conic sections?

Answer: All conic sections can be projected into each other

With the appropriate projection, all conic sections are projections of each other.

16. Connie also loves inversive geometry. How are the conic sections defined in inversive geometry? "A conic section is the inverse of a ________ in a _________."

Answer: circle, circle

In inversive geometry, we are always inverting things in a circle (the aptly named, 'circle of inversion'). The inverse of a circle in a circle, depending on where the circle is located, is always a conic section.

Answer: AC is greater than 0, A is not equal to C

The values of A and C determine what type of conic the graph is. If A equals C, the conic is a circle. If AC is lessthan 0 (ie one is positive, one is negative) then the conic is a hyperbola. If AC = 0, ie one of A or C is 0 (but not both), then the conic is a parabola.

18. The ellipse and the hyperbola both have a "major axis" and a "minor axis".

Answer: True

The ellipse and the hyperbola have exactly 2 lines of symmetry; the longer one is the major axis and the shorter one is the minor axis. They intersect at the center of the conic. The parabola has one line of symmetry, and the circle has an infinite number. The Latin name for the minor axis is "latus rectum", which always sets Connie into a fit of giggles.

19. Connie knows that there are four types of quadratic relations. Approximately how many types of cubic relations are there?

Answer: 43

Newton and Euler both failed to classify all cubic curves. (They each left one or two out by mistake). It's amazing to think that there are only 4 quadratic curves, but well over 40 cubic curves! Connie passes out when she thinks about how many quartic (degree 4) curves there could be!

20. Polly asked Connie what her favourite conic section is. "Well, Polly, I love them all! But my absolute favourite is the one with the asymptotes." Which conic section is Connie's favourite?

Answer: The hyperbola - the only one with asymptotes

The graceful, two-branched hyperbola is the only non-continuous asymptotic conic section. Connie hopes you liked her quiz!

Source: Author Mrs_Seizmagraff

This quiz was reviewed by FunTrivia editor crisw before going online.
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