28.5k views
2 votes
Find the equation of the ellipse with a horizontal major axis and an area of exactly 264 square centimeters.

1 Answer

1 vote

Final answer:

To find the equation of an ellipse with a horizontal major axis and a given area, use the formula A = pi * a * b, where a is the length of the semi-major axis and b is the length of the semi-minor axis. Rearrange the formula to solve for b, and substitute the given values to find the equation of the ellipse.

Step-by-step explanation:

To find the equation of an ellipse with a horizontal major axis and a given area, we can use the formula for the area of an ellipse: A = pi * a * b, where a is the length of the semi-major axis and b is the length of the semi-minor axis. In this case, we are given the area as 264 square centimeters. Since the major axis is horizontal, the length of the semi-major axis will be half of the major axis, which is a = 16/2 = 8 cm. We can rearrange the formula to solve for b: b = A / (pi * a). Substituting the given values, we have b = 264 / (pi * 8).

Therefore, the equation of the ellipse is (x^2 / 64) + (y^2 / (264 / (pi * 8))^2) = 1.

User Mayur Satav
by
8.6k points