Given equation is
[tex]\frac{x^2}{9}-\frac{y^2}{16}=1[/tex]
It can be written as follows.
[tex]\frac{x^2}{3^2}-\frac{y^2}{4^2}=1[/tex]
Which is of the form
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]
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)
[tex]c=\sqrt[]{a^2+b^2}[/tex]
Substitute a=3 and b=4, we get
[tex]c=\sqrt[]{3^2+4^2}=\sqrt[]{9+16}=\sqrt[]{25}=5[/tex]
Substitute c=5, we get
Hence the foci are (5,0) and (-5,0).
