Find the vertices foci and asymptotes of the hyperbola y2 9

Find the vertices, foci, and asymptotes of the hyperbola y2 9 x2 16 = 1. (Enter your asymptotes as a comma-separated list of equations.)

vertex (x, y) = (smaller y-value)

vertex (x, y) = (larger y-value)

focus (x, y) = (smaller y-value)

focus (x, y) = (larger y-value)

asymptotes

Sketch the graph of the hyperbola.

Solution

y²/9 -x²/16=1

Here the centre (h,k) is (0,0)

Here a^2=9   and b^2=16

Vertices= (h,k+-a)=(0,+-3)

smaller value (0,-3)

larger value (0,3)

c^2=a^2 + b^2= 25

focii= (h,k+-c)= (0,+-5)

smaller value = (0,-5)

larger value (0,5)