Write an equation of an ellipse in standard form with the center at the origin and with the given vertex at (-3,0) and co-vertex at (0,2)

Solution:

An ellipse is the locus of all those points in a plane such that the sum of their distances from two fixed points in the plane, is constant.

Given: Vertex = (-3, 0)

Co-vertex = (0, 2)

Where the center (h, k) = (0, 0)

a = -3, b = 2

We know that,

Standard form of the ellipse is (x - h)²/a² + (y - k)²/b² = 0

Substituting the values

(x - 0)²/(-3)² + (y - 0)²/2² = 0

So we get,

x²/9 + y²/4 = 0

Therefore, the equation of an ellipse in standard form is x²/9 + y²/4 = 0.

Write an equation of an ellipse in standard form with the center at the origin and with the given vertex at (-3,0) and co-vertex at (0,2)

Summary:

The equation of an ellipse in standard form with the center at the origin and with the given vertex at (-3,0) and co-vertex at (0,2) is x²/9 + y²/4 = 0.