Question

an ellipse has a center at the origin , a vertex along the major axis at (13,0), and a focus at (12,0). What is the equation of the ellipse?

Answer 1

Answer:

The answer to your question is below

Step-by-step explanation:

Data

Center = (0, 0)

Vertex = (13, 0)

Focus = (12, 0)

Process

From the data we know that it is a horizontal ellipse.

1.- Calculate "a", the distance from the center to the vertex.

                  a = 13

2.- Calculate "c", the distance from the center to the focus

                  c = 12

3.- Calculate b

Use the Pythagorean theorem to find it

                  a² = b² + c²

-Solve for b

                  b² = a² - c²

-Substitution

                  b² = 13² - 12²

-Simplification

                  b² = 169 - 144

                  b² = 25

                  b = 5

4.- Find the equation of the ellipse

                       $\frac{x^{2} }{13^{2}} + \frac{y^{2}}{5^{2}} = 1$    or $\frac{x^{2} }{169} + \frac{y^{2}}{25} = 1$