Practice - Standard Equation of an Ellipse
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Practice Questions
Test your understanding with targeted questions
Write the standard equation of an ellipse with semi-major axis 4 and semi-minor axis 2.
💡 Hint: Use the formula \\( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1 \\).
What is the length of the semi-major axis of an ellipse if \( a = 5 \)?
💡 Hint: Refer to the variable \\( a \\) in the equation.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the standard form of an ellipse centered at the origin?
💡 Hint: Focus on the role of \\( a \\) and \\( b \\).
True or False: The foci of an ellipse are always located on the minor axis.
💡 Hint: Consider how the axes are defined in an ellipse.
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Challenge Problems
Push your limits with advanced challenges
Design an elliptical garden using a semi-major axis of 8 and a semi-minor axis of 3. Write down the equation and describe the distance between the foci.
💡 Hint: Remember to apply the equation for focal distance.
An astronomer wants to track an elliptical orbit with a focus at the sun. If the semi-major axis is 10 million kilometers, and the semi-minor axis is 8 million kilometers, find the foci and write the standard equation.
💡 Hint: Do not forget the equations for \\( c \\) and the standard form.
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Reference links
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