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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
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 \\).
Question 2
Easy
What is the length of the semi-major axis of an ellipse if \( a = 5 \)?
💡 Hint: Refer to the variable \\( a \\) in the equation.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the standard form of an ellipse centered at the origin?
- \\( \\frac{y^2}{a^2} + \\frac{x^2}{b^2} = 1 \\)
- \\( \\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1 \\)
- \\( x^2 + y^2 = r^2 \\)
💡 Hint: Focus on the role of \\( a \\) and \\( b \\).
Question 2
True or False: The foci of an ellipse are always located on the minor axis.
- True
- False
💡 Hint: Consider how the axes are defined in an ellipse.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation