Grade 10 Ellipse Worksheet
This worksheet covers key concepts of ellipses, including their equations, foci, vertices, and graphing.
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Grade 10 Ellipse Worksheet
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. What is the standard form equation of an ellipse centered at the origin?
x²/a² - y²/b² = 1
x²/a² + y²/b² = 1
(x-h)²/a² + (y-k)²/b² = 1
y = ax² + bx + c
2. For an ellipse, which of the following is true about its foci?
They are points on the minor axis.
They are equidistant from the center.
The sum of the distances from any point on the ellipse to the foci is constant.
Both b and c
3. The longest diameter of an ellipse is called the .
4. The distance from the center to a focus of an ellipse is denoted by .
5. Find the vertices and foci of the ellipse with the equation x²/25 + y²/9 = 1.
6. Write the standard form equation of an ellipse with a major axis of length 10 along the x-axis and a minor axis of length 6.
7. Graph the ellipse given by the equation x²/36 + y²/16 = 1. Clearly label the center, vertices, and foci.
8. True or False: The eccentricity of an ellipse is always greater than 1.
True
False
9. True or False: If the major axis is horizontal, then a² is under the x² term in the standard equation.
True
False
10. An elliptical archway is 16 feet wide at its base and 10 feet high in the center. Write the equation of the ellipse that models this archway.