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

Practice: Hyperbola

Lesson 6.5Conic Sections

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8 questions

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Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the standard equation of a hyperbola centered at the origin?
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Recall the form for hyperbolas and what the variables represent.
Question 2.
Define what a focus is in relation to a hyperbola.
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Consider how foci are essential to conic sections.
3Question 3.
What is the standard equation for a hyperbola centered at the origin?
- $$ \\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1 $$
- $$ \\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1 $$
- $$ \\frac{y^2}{a^2} - \\frac{x^2}{b^2} = -1 $$
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Pay attention to the signs in the equation.
4Question 4.
True or False: The eccentricity of a hyperbola is always less than one.
- True
- False
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Recall the definition of eccentricity for different conic sections.
Question 5.
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.
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Use the relationship for calculating the foci c = √(a² + b²) and the standard form for asymptotes.
Question 6.
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.
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Recall that a^2 + b^2 = c^2 to find c first.

4 more questions in this section. Enroll free to practise them all.