Practice Hyperbola (6.5) - Conic Sections - ICSE 11 Maths
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Hyperbola

Practice - Hyperbola

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Learning

Practice Questions

Test your understanding with targeted questions

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.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

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.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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.

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