Practice - Standard Equation of a Hyperbola
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Practice Questions
Test your understanding with targeted questions
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 $a^2 = 9$.
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.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the standard equation for a hyperbola with the transverse axis along the x-axis?
💡 Hint: Consider the orientation of the hyperbola.
Is it true that the vertices of a hyperbola lie on the transverse axis?
💡 Hint: Recall the geometric definition of a hyperbola.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
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 $b$.
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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