Question

An ellipse has a vertex at (4, 0), a co-vertex at (0, 2), and a center at the origin. Which is the equation of the ellipse in standard form?

Answer 1

Answer:

x^2/ 16 + y^2/4 = 1

Step-by-step explanation:

The major axis is 4 and that goes with the x variable.  It is the major axis because 4 is a larger value than 2.

4 x 4 = 16

2 x 2 = 4

Answer 2

The equation of the ellipse in standard form is x² / 16 + y² / 4 = 1.

How to derive the standard form of the equation of the ellipse

In this problem we know the coordinates of a vertex, a co-vertex and the center of an ellipse. Based on this information, we find an ellipse whose major axis is parallel to the x-axis. whose formula in standard form is:

(x - h)² / a² + (y - k)² / b² = 1     (1)

Where:

• (h, k) - Center of the ellipse
• a - Major semiaxis length
• b - Minor semiaxis length

The major semiaxis has a length of 4 units and the minor semiaxis has a length of 2 units. If we know that (h, k) = (0, 0), a = 4 and b = 2, then the equation of the ellipse is:

x² / 16 + y² / 4 = 1

The equation of the ellipse in standard form is x² / 16 + y² / 4 = 1.

To learn more on ellipses: https://brainly.com/question/19507943

#SPJ1