Question

Find the vertices and foci of the hyperbola.y2 − x2 = 9vertices (x, y) = (smaller y-value)(x, y) = (larger y-value)foci (x, y) = (smaller y-value)(x, y) = (larger y-value)

Answer 1

Explanation:

Given is a hyperbola as

`y^2-x^2 =9\\(y^2)/(9) -frac{x^2}{9}=1`

This is of the std form where a=b=3

Hence vertices are

`(x,y) =(3,-3) and (3,3)\\`

Foci =( ±ae,0)

=(±
`√(a^2+b^2) ,0)\\`

=(±
`2√(3) ,0)`