Question

Write an equation in standard form of an ellipse that has a vertex at (−6, 0), a co-vertex at (0, 5), and a center at the origin

Answer 1

To find the equation of an ellipse in standard form, we need the coordinates of the center, (h, k), and the lengths of the semi-major axis, a, and the semi-minor axis, b.

Given that the center is at the origin (0,0), we have h = 0 and k = 0.

The semi-major axis is the distance between the center and the vertex, so a = 6.

The semi-minor axis is the distance between the center and the co-vertex, so b = 5.

The standard form of an ellipse with its center at the origin is:

x^2/a^2 + y^2/b^2 = 1

Plugging in the values for a and b, we get:

x^2/6^2 + y^2/5^2 = 1

Simplifying, we have:

x^2/36 + y^2/25 = 1

Therefore, the equation in standard form for the given ellipse is:

x^2/36 + y^2/25 = 1