What is an equation in standard form of an ellipse centered at the origin with vertex (-6, 0) and covertex (0, 4)?

Solution:

An ellipse is the locus of points in a plane, the sum of whose distances from two fixed points is a constant value. The two fixed points are called the foci of the ellipse.

The standard equation of an ellipse is (x - h)²/(a²) + (y - k)²/(b²) = 1

Where, a is the vertex

b is the co-vertex

Given, ellipse is centred at origin

Thus, (h, k) = (0, 0)

Vertex = (-6, 0)

So, the length of a is -6.

Co-vertex = (0, 4)

So, the length of b is 4.

Now, the equation of the ellipse will be

(x - 0)²/(-6)² + (y - 0)²/(4)² = 1

x²/36 + y²/16 = 1

Therefore, the equation of the ellipse is x²/36 + y²/16 = 1.

What is an equation in the standard form of an ellipse centered at the origin with vertex (-6, 0) and covertex (0, 4)?

Summary:

An equation in standard form of an ellipse centered at the origin with vertex (-6, 0) is x²/36 + y²/16 = 1.