Solve and practice you skills with 7 ellipse exercises and problems . These problems cover a range of concepts related to ellipses, including perimeter, area, eccentricity, and the calculation of semi-major and semi-minor axes.
1. Perimeter Calculation: Given an ellipse with a semi-major axis (a) of 12 inches and a semi-minor axis (b) of 8 inches, calculate the approximate perimeter using all three perimeter formulas: P ≈ π(a + b), P ≈ π√[2(a² + b²)], and P ≈ π[(3/2)(a + b) - √(ab)].
2. Area Calculation: Find the area of an ellipse with a semi-major axis (a) of 5 meters and a semi-minor axis (b) of 3 meters.
3. Eccentricity Calculation: Determine the eccentricity of an ellipse with a semi-major axis (a) of 10 feet and a semi-minor axis (b) of 6 feet.
4. Latus Rectum Calculation: Calculate the length of the latus rectum for an ellipse with a semi-major axis (a) of 7 inches and a semi-minor axis (b) of 5 inches.
5. Semi-Major Axis Calculation: Given the area (A) of an ellipse as 100 square centimeters and the semi-minor axis (b) as 4 centimeters, find the length of the semi-major axis (a).
6. Semi-Minor Axis Calculation: If the area (A) of an ellipse is 150 square meters, and the semi-major axis (a) is 10 meters, determine the length of the semi-minor axis (b).
7. Real-Life Application: Imagine an elliptical racetrack with a length of 200 meters along the semi-major axis and a width of 50 meters along the semi-minor axis. Calculate the perimeter of this racetrack to determine the distance a runner needs to cover when running around the track.