Question

Which of the following statements about conic sections is always correct?

A. If a line intersects a conic section, then it will intersect the conic section at exactly one point.

B. If a line intersects a conic section, then it will intersect the conic section at exactly two points.

C. If a line intersects a conic section, then it will intersect the conic section in more than two points.

D. A parabola and a hyperbola drawn in a plane will always intersect.

E. A line can cross a parabola once, twice, or not at all.

Answer 1

@mathstudent55 @Hero

Answer 2

@IloveCharlie, which do you believe is correct?

Answer 3

I don't know... B????

Answer 4

You have to think about it a bit more.

Answer 5

C?

Answer 6

I was trying to show you a demonstration of the problem. Hang on

Answer 7

https://www.desmos.com/calculator/4gj5ishgdy

Answer 8

@IloveCharlie are you still here?

Answer 9

Yup.

Answer 10

I sent you a link to demonstrate a scenario. As you can see, a line can intersect a conic at only one point or it doesn't have to intersect it at all.

Answer 11

Oh so it is A? :D

Answer 12

wait, no

Answer 13

You have to understand what it is saying.

Answer 14

There's more than one possibility when it comes to a line and a conic. It can intersect at zero points, one point, or two points. So that basically eliminates A, B, and C.

Answer 15

Ah. So it's D?

Answer 16

https://www.desmos.com/calculator/tzu7akazui

Answer 17

Lol okay.. So it is E?

Answer 18

Yes, finally...

https://www.desmos.com/calculator/wtmg9qy5hp

Answer 19

lol alright. Thank you!