Question

Guys please help me with this

Answer 1

Answer:

The equation of the elipse is

$\frac{x^2}{169} + \frac{y^2}{25} = 1$

Step-by-step explanation:

Equation of an elipse:

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

$\frac{(x - x_c)^2}{a^2} + \frac{(y - y_c)^2}{b^2} = 1$

Centre at (0,0):

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

So

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

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

$\frac{x^2}{169} + \frac{y^2}{25} = 1$