# Lesson Worksheet: Equation of an Ellipse Mathematics • 10th Grade

In this worksheet, we will practice finding the equation of an ellipse using different givens and using it to solve problems that involve ellipse-shaped constructions.

Q1:

Derive the equation of an ellipse with foci at the points and , which has a major axis of length 15.

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Q2:

An ellipse has a vertex at and a covertex at . The major axis of the ellipse is parallel to the . What is the equation of the ellipse?

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Q3:

Derive the equation of an ellipse centered at the origin with foci at the points and , which has a major axis of length 10.

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Q4:

Derive the equation of an ellipse centered at the origin with foci at the points and , which has its vertices at the points and .

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Q5:

Fill in the blank: The ellipse has a major axis of length cm.

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Q6:

Given that the simultaneous equations are graphically represented in the figure, solve the two equations and find the most accurate estimations of - and -values. • A and , and
• B and , and
• C and , and
• D and , and
• E and , and

Q7:

What is the equation of an ellipse that has a semimajor axis, which is parallel to the , of length 10 and foci points and ?

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Q8:

Let , , and be the coordinates of the center, a focus, and a covertex of an ellipse respectively. What is the equation describing this ellipse?

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Q9:

An ellipse has the equation . If the major axis is reduced to half, the minor axis is doubled, and the center does not change, what will the equation of the new ellipse be?

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Q10:

Let be an ellipse whose equation is given by . If is another ellipse with its center at the focus of that is closer to the origin and has the same length of major and minor axes as , derive the equation of .

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This lesson includes 1 additional question and 54 additional question variations for subscribers.