What is an equation in standard form of an ellipse centered at the origin with vertex (-7, 0) and co-vertex(0, 5)?

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 = (-7,0)

So, the length of a is -7.

Co-vertex = (0,5)

So, the length of b is 5.

Now, the equation of the ellipse will be

(x - 0)² / (-7)² + (y - 0)² / (5)² = 1

x² / 49 + y² / 25 = 1

Therefore, the equation of the ellipse is x² / 49 + y² / 25 = 1.

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What is an equation in standard form of an ellipse centered at the origin with vertex (-7, 0) and co-vertex(0, 5)?

Summary:

An equation in standard form of an ellipse centered at the origin with vertex (-7, 0) and co-vertex (0, 5) is x² / 49 + y² / 25 = 1.