Grade 12 Math: Ellipses Worksheet
This worksheet covers key concepts of ellipses, including their standard equations, foci, vertices, and eccentricity, suitable for Grade 12 math students.
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Grade 12 Math: Ellipses Worksheet
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. Which of the following 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
(x-h)²/a² - (y-k)²/b² = 1
2. The sum of the distances from any point on an ellipse to its two foci is always equal to:
2a
2b
2c
a+b
3. The of an ellipse is the ratio c/a, which measures how 'stretched out' the ellipse is.
4. For an ellipse, the major axis is always than the minor axis.
5. The points at the ends of the major axis are called the .
6. For the ellipse with the equation x²/25 + y²/9 = 1, identify the following:
a. Center:
b. Vertices:
c. Co-vertices:
d. Foci:
e. Length of Major Axis:
f. Length of Minor Axis:
7. Sketch the graph of the ellipse from question 6 on the coordinate plane below, labeling the center, vertices, and foci.
8. Write the standard form equation of an ellipse with foci at (-4, 0) and (4, 0) and vertices at (-5, 0) and (5, 0).
9. An ellipse has a center at (1, -2), a major axis length of 10 along the y-axis, and a minor axis length of 6. Write its standard form equation.
10. The eccentricity of an ellipse is always greater than 1.
True
False
11. If the major axis is horizontal, the 'a' value is associated with the x-term in the standard equation.
True
False
12. The ceiling of a whispering gallery is in the shape of a semi-elliptical arch. The gallery is 120 feet long and the ceiling is 30 feet high at the center. How far from the walls are the foci located?