Grade 9 Ellipses Worksheet
This worksheet covers the fundamental concepts of ellipses, including their definition, standard equations, foci, vertices, and eccentricity.
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Grade 9 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. An ellipse is the set of all points in a plane such that the sum of the distances from two fixed points, called the , is constant.
2. The longest diameter of an ellipse is called the , and the shortest diameter is called the .
3. The standard form of the equation of an ellipse centered at the origin with a horizontal major axis is .
4. Which of the following is the standard equation of an ellipse centered at (h, k) with a vertical major axis?
(x-h)²/a² + (y-k)²/b² = 1
(x-h)²/b² + (y-k)²/a² = 1
(x-k)²/a² + (y-h)²/b² = 1
(y-k)²/b² + (x-h)²/a² = 1
5. What is the eccentricity of an ellipse with a = 5 and c = 3?
0.5
0.6
0.75
0.8
6. Find the vertices and foci of the ellipse given by the equation x²/25 + y²/9 = 1.
7. Write the equation of an ellipse centered at the origin with a major axis of length 10 along the y-axis and a minor axis of length 6.
8. Sketch the graph of the ellipse (x-1)²/4 + (y+2)²/9 = 1 on the coordinate plane below.