Practice Standard Equation Of A Hyperbola (6.5.1) - Conic Sections - ICSE 11 Maths

Practice: Standard Equation of a Hyperbola

Lesson 6.5.1Conic Sections

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10 questions

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6 sample questions

Question 1.
Write the standard equation for a hyperbola centered at the origin with vertices (3, 0) and (-3, 0).
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Remember, the distance to the vertices is $a = 3$, so $a^2 = 9$.
Question 2.
What are the asymptotes of a hyperbola represented by $\frac{x^2}{16} - \frac{y^2}{25} = 1$ ?
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Use $y = \\pm \\frac{b}{a}x$ and identify $b$ and $a$ from the equation.
3Question 3.
What is the standard equation for a hyperbola with the transverse axis along the x-axis?
- $\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1$
- $\\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1$
- $\\frac{y^2}{a^2} - \\frac{x^2}{b^2} = 1$
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Consider the orientation of the hyperbola.
4Question 4.
Is it true that the vertices of a hyperbola lie on the transverse axis?
- True
- False
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Recall the geometric definition of a hyperbola.
Question 5.
A hyperbola has foci at (3, 0) and (-3, 0) and a distance of 4 from the center to each vertex. Write its equation.
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Identify $c$ from the foci and then find $b$.
Question 6.
Given a hyperbola $\frac{x^2}{49} - \frac{y^2}{36} = 1$ , calculate the eccentricity.
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Utilize the eccentricity formula and find $c$.

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