Question

Guys please help me with this

Answer 1

The equation of the elipse is

`(x^2)/(169) + (y^2)/(25) = 1`

Explanation:

Equation of an elipse:

The equation of a elipse with centre
`(x_c,y_c)` has the following format:

`((x - x_c)^2)/(a^2) + ((y - y_c)^2)/(b^2) = 1`

Centre at (0,0):

Means that
`(x_c,y_c) = (0,0)`.

So

`(x^2)/(a^2) + (y^2)/(b^2) = 1`

Vertex at (13,0):

Vertex at 13 means that
`a = 13, a^2 = 13^2 = 169`

Focus at (-12,0):

Means that
`c = 12, c^2 = 12^2 = 144`

We have that:

`a^2 = b^2 + c^2`

So

`169 = b^2 + 144`

`b^2 = 25`

So, the equation of the elipse is

`(x^2)/(169) + (y^2)/(25) = 1`