Question

Find an equation of the hyperbola having foci at (-4,-3) and (-4, 7) and vertices at (-4,-1) and (-4,5).

Answer 1

We are given

`\begin{gathered} Foci=(-4,-3),(-4,7) \\ Vertices=(-4,-1),(-4,5) \\ From\text{ the above information} \\ a=3 \\ c=(7-(-3))/(2)=5 \\ b^2=c^2-a^2=5^2-(3)^2 \\ b^2=25-9 \\ b^2=16 \\ b=4 \\ centre=((-4-4)/(2),(-3+7)/(2)) \\ centre=(-4,2) \\ Equation\text{ of hyperbola} \\ ((y-2)^2)/(9)-((x+4)^2)/(16)=1 \end{gathered}`