Question

Find the vertices and foci of the hyperbola with equation (x-5)^2/81 -(y-1)^2/144 = 1

Answer 1

The foci is (+15,0),(-15,0) and the vertices is (+9,0),(-9,0)

Answer 2

Given the equation of an hyperbola in the form:
$\frac{(x-a)^2}{b^2}- \frac{(y-c)^2}{d^2}=1$
Then the focus of the hyperbola is $(\pm\sqrt {b^2+d^2},0)$
Compute like this:
$\sqrt{81+144}=15$
So the two focus points are $(\pm15,0)$
The vertices are given by the formula: $(\pm a,0)$
We deduce the two vertices of the given hyperbola: $(\pm9,0)$
since $\sqrt{81}=9$