Question 867669
Find the equation of a hyperbola with a vertex at (-2,15) , a focus at (-2,22) and a center at (-2,7)
Given data shows hyperbola has a vertical transverse axis.
Its standard form of equation: {{{(y-k)^2/a^2-(x-h)^2/b^2=1}}}, (h,k)=coordinates of center
center:(-2,7)
a=8 (distance from center to vertices on the vertical transverse axis)
a^2=64
c=15 (distance from center to foci on the vertical transverse axis)
c^2=225
c^2=a^2+b^2
b^2=c^2-a^2=225-64=161
equation of given hyperbola:  {{{(y-7)^2/64-(x+2)^2/161=1}}}