Find the standard form of the equation of the hyperbola sati

Find the standard form of the equation of the hyperbola satisfying the given conditions. Center. (6, - 4); focus: (10, - 4); vertex: (9, - 4) The equation is

Solution

Solution:

Given hyperbola has a vertical transverse axis.
Its standard form of equation (x-k)² /a² + (y-h)²/b² =1

(h,k)=(x,y) coordinates of center
center: (6,-4)

a=3 (distance from center to vertex, (6,-4 ) to (9,-4))
a^2=9

c=4 (distance from center to focus, (6,-4 ) to (10,-4)
c^2=16

c^2=a^2+b^2
b^2=c^2-a^2

=16-9

=7
Equation of given hyperbola

(x+4)² /7 + (y-6)²/7 =1

answer