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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the standard equation of a hyperbola centered at the origin?
💡 Hint: Recall the form for hyperbolas and what the variables represent.
Question 2
Easy
Define what a focus is in relation to a hyperbola.
💡 Hint: Consider how foci are essential to conic sections.
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 centered at the origin?
- $$ \\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1 $$
- $$ \\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1 $$
- $$ \\frac{y^2}{a^2} - \\frac{x^2}{b^2} = -1 $$
💡 Hint: Pay attention to the signs in the equation.
Question 2
True or False: The eccentricity of a hyperbola is always less than one.
- True
- False
💡 Hint: Recall the definition of eccentricity for different conic sections.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Find the coordinates of the foci for the hyperbola given by $$ \frac{x^2}{25} - \frac{y^2}{16} = 1 $$ and also the equations of the asymptotes.
💡 Hint: Use the relationship for calculating the foci c = √(a² + b²) and the standard form for asymptotes.
Question 2
A hyperbola has vertices at (±6, 0) and foci at (±√(36 + b^2), 0). If b is known to be 8, write the equation of the hyperbola.
💡 Hint: Recall that a^2 + b^2 = c^2 to find c first.
Challenge and get performance evaluation