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

`(x^2)/(9)-(y^2)/(16)=1`

It can be written as follows.

`(x^2)/(3^2)-(y^2)/(4^2)=1`

Which is of the form

`(x^2)/(a^2)-(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).