# 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}/a^{2} + (y - k)^{2}/b^{2} = 0

Substituting the values

(x - 0)^{2}/(-3)^{2} + (y - 0)^{2}/2^{2} = 0

So we get,

x^{2}/9 + y^{2}/4 = 0

Therefore, the equation of an ellipse in standard form is x^{2}/9 + y^{2}/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 x^{2}/9 + y^{2}/4 = 0.