Question

How to find the equation of an ellipse?

a) Use the formula x²/a² + y²/b² = 1 for a horizontal ellipse.
b) Employ the formula (x-h)²/a² + (y-k)²/b² = 1 for an ellipse centered at (h, k).
c) Set the equation equal to zero and solve for x to obtain the ellipse.
d) Determine the foci by calculating the square root of (a² - b²).

Answer 1

To find the equation of an ellipse, use the formula (x-h)²/a² + (y-k)²/b² = 1 for an ellipse centered at (h, k) or x²/a² + y²/b² = 1 for a horizontal ellipse. Hence the correct answer is option A

Step-by-step explanation:

An ellipse can be represented by an equation in the form (x-h)²/a² + (y-k)²/b² = 1, where (h, k) represents the center of the ellipse, a is the length of the semi-major axis, and b is the length of the semi-minor axis. This formula is used for an ellipse centered at (h, k). If the ellipse is horizontally oriented, meaning its major axis lies on the x-axis, the equation can be simplified to x²/a² + y²/b² = 1. To find the equation of an ellipse, you need the center, the lengths of the semi-major and semi-minor axes, and whether the ellipse is horizontally or vertically oriented.

Hence the correct answer is option A