What is an equation in standard form of an ellipse centered at the origin with vertex (-5, 0) and covertex at (0, 4).

Solution:

Given vertex(-5, 0) and centre is origin

Hence, (h, k) = (0,0); a = -5 and b = 4

The standard form of the ellipse with horizontal major axis is

(x - h)²/a² + (y - k)²/b² = 1

(x - 0)²/5² + (y-0)²/4² = 1

x²/25 + y²/16 = 1

Take LCM of the fractions

16x² + 25y² = 16(25)

16x² + 25y² = 400

The equation of ellipse is 16x² + 25y² = 400

What is an equation in standard form of an ellipse centered at the origin with vertex (-5, 0) and covertex at (0,4).

Summary:

The equation in standard form of an ellipse centered at the origin with vertex (-5, 0) and covertex at (0,4) is 16x² + 25y² = 400.