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
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