How do you write the equation of the hyperbola given Foci: (0,-7),(0,7) and vertices (0,-3), (0,3)?

1 Answer
Dec 13, 2016

The equation is y^2/9-x^2/40=1y29x240=1

Explanation:

The foci are F=(0,7)F=(0,7) and F'=(0,-7)

The vertices are A=(0,3) and A'=(0,-3)

So, the center is C=(0,0)

So, a=3

c=7

and b=sqrt(c^2-a^2)=sqrt(49-9)=sqrt40

Therefore, the equation of the hyperbola is

y^2/a^2-x^2/b^2=1

y^2/9-x^2/40=1

graph{(y^2/9-x^2/40-1)=0 [-11.25, 11.25, -5.625, 5.625]}