Find the center vertices foci and the equations of the asymp

Find the center, vertices, foci, and the equations of the asymptotes of the hyperbola. (If an answer does not exist, enter DNE) x^2/9 - y^2/4 = 1 center (x, y) = vertices (x, y) = (smaller x-value) (x, y) = (larger x-value) foci (x, y) = (smaller x-value) (x, y) = (larger x-value) asymptotes (negative slope) (positive slope) Sketch the hyperbola using the asymptotes as an aid.

Solution

Here centre=(0,0)

And vertices =(+-3,0)

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

Here a=3 and b=2

Therefore c=sqrt(a^2 + b^2)=sqrt 13

Hence focii= (sqrt13,0),(-sqrt13,0)

smaller value= (-sqrt13,0)

larger value=(sqrt13,0)

Equation of asymptote is

y=+-(b/a)(x-h) +k

y= +-2x/3

negative slope

y=-2x/3

positive slope

y=2/3