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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Write the standard equation for a hyperbola centered at the origin with vertices (3, 0) and (-3, 0).
💡 Hint: Remember, the distance to the vertices is $a = 3$, so $a^2 = 9$.
Question 2
Easy
What are the asymptotes of a hyperbola represented by $\frac{x^2}{16} - \frac{y^2}{25} = 1$?
💡 Hint: Use $y = \\pm \\frac{b}{a}x$ and identify $b$ and $a$ from 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 equation for a hyperbola with the transverse axis along the x-axis?
- $\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1$
- $\\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1$
- $\\frac{y^2}{a^2} - \\frac{x^2}{b^2} = 1$
💡 Hint: Consider the orientation of the hyperbola.
Question 2
Is it true that the vertices of a hyperbola lie on the transverse axis?
- True
- False
💡 Hint: Recall the geometric definition of a hyperbola.
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Challenge Problems
Push your limits with challenges.
Question 1
A hyperbola has foci at (3, 0) and (-3, 0) and a distance of 4 from the center to each vertex. Write its equation.
💡 Hint: Identify $c$ from the foci and then find $b$.
Question 2
Given a hyperbola $\frac{x^2}{49} - \frac{y^2}{36} = 1$, calculate the eccentricity.
💡 Hint: Utilize the eccentricity formula and find $c$.
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