Question

Consider the conic section C represented by the equation 9x2 – 25y2 = 225. Which of these is a characteristic of the graph of C? (A) Vertices at (3,0) (B) Vertices at (0, 5) (C) Asymptotes at y = + x (D) Asymptotes at y = x 3​

Answer 1

The only true statement is:

(B) Vertices at (0, 5)

Explanation:

We have the equation:

9*x^2 - 25*y^2 = 225

The graph of this equation can be seen below.

In the graph we can see:

We have two vertices, one at (0, 5) and another at (0, - 5)

Then option B) "Vertices at (0, 5)" is true.

Also in the graph you can see that we have (kinda linear) asymptotes at:

y = x + 5

y = -x + 5

y = x - 5

y = -x - 5

The two options for the asymptotes are:

(C) Asymptotes at y = + x

(D) Asymptotes at y = x 3​

So both of these are incorrect.