Ellipses Worksheet - Grade 10 Math

This worksheet provides practice problems on the properties, equations, and graphing of ellipses for Grade 10 math students.

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Includes

3 Short AnswerFill in the BlanksMultiple ChoiceTrue / False

Standards

CCSS.MATH.CONTENT.HSA.APR.D.6CCSS.MATH.CONTENT.HSG.GPE.A.3

8 sections · Free to use · Printable

Ellipses: Properties and Equations

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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.

1. Define an ellipse in your own words, including its key components.

2. What is the relationship between the major axis, minor axis, and foci of an ellipse?

3. The standard form of the equation of an ellipse centered at the origin is .

4. The foci of an ellipse lie on its .

5. The distance from the center to a focus is denoted by .

6. Which of the following is the equation of an ellipse centered at (h, k)?

$(x-h)^2/a^2 + (y-k)^2/b^2 = 1$

$(x+h)^2/a^2 - (y+k)^2/b^2 = 1$

$x^2/a^2 + y^2/b^2 = 1$

$(x-h)^2/a^2 - (y-k)^2/b^2 = 0$

7. If the major axis of an ellipse is horizontal, which variable is associated with 'a' in the standard equation?

8. Graph the ellipse given by the equation: $x^2/25 + y^2/9 = 1$. Label the center, vertices, and foci.

9. Write the standard form of the equation of an ellipse with foci at $(\pm 4, 0)$ and vertices at $(\pm 5, 0)$.

10. The sum of the distances from any point on an ellipse to the two foci is constant.

True

False