Question

Fill in each blank so that the resulting statements are true.The vertices of The foci are located at ____.

Answer 1

Given equation is

$\frac{x^2}{9}-\frac{y^2}{16}=1$

It can be written as follows.

$\frac{x^2}{3^2}-\frac{y^2}{4^2}=1$

Which is of the form

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

where a=3 and b=4.

We know that the coordinates of the vertices are (a,0) and (-a,0)

Substitute a=3, we get

The vertices are (3,0) and (-3,0).

We know that the coordinates of the foci are (c,0) and (-c,0)

$c=\sqrt[]{a^2+b^2}$

Substitute a=3 and b=4, we get

$c=\sqrt[]{3^2+4^2}=\sqrt[]{9+16}=\sqrt[]{25}=5$

Substitute c=5, we get

Hence the foci are (5,0) and (-5,0).