SATHEE: Hyperbola 2 Question 3

Hyperbola 2 Question 3

3. If the eccentricity of the standard hyperbola passing through the point $(4, 6)$ is 2 , then the equation of the tangent to the hyperbola at $(4, 6)$ is (2019 Main, 8 April II)

(a) $3 x - 2 y = 0$

(b) $x - 2 y + 8 = 0$

(d) $2 x - 3 y + 10 = 0$

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Answer:

Correct Answer: 3. (c)

Solution:

Let the equation of standard hyperbola is

$\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$

Now, eccentricity of hyperbola is

$\sqrt{1 + \frac{b^{2}}{a^{2}}} = 2$

$\Rightarrow a^{2} + b^{2} = 4 a^{2}$

$\Rightarrow b^{2} = 3 a^{2}$

Since, hyperbola (i) passes through the point $(4, 6)$

$∴ \frac{16}{a^{2}} - \frac{36}{b^{2}} = 1$

On solving Eqs. (ii) and (iii), we get

$a^{2} = 4 and b^{2} = 12$

Now, equation of tangent to hyperbola (i) at point $(4, 6)$ , is

$\begin{aligned} \frac{4 x}{a^{2}} - \frac{6 y}{b^{2}} = 1 \\ \Rightarrow & \frac{4 x}{4} - \frac{6 y}{12} = 1 \\ \Rightarrow & x - \frac{y}{2} = 1 \Rightarrow 2 x - y - 2 = 0 \end{aligned} [from Eq. (iv)]$

Hyperbola 2 Question 3

3. If the eccentricity of the standard hyperbola passing through the point $(4, 6)$ is 2 , then the equation of the tangent to the hyperbola at $(4, 6)$ is (2019 Main, 8 April II)

Answer:

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Hyperbola 2 Question 3

3. If the eccentricity of the standard hyperbola passing through the point (4,6) is 2 , then the equation of the tangent to the hyperbola at (4,6) is (2019 Main, 8 April II)

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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3. If the eccentricity of the standard hyperbola passing through the point $(4, 6)$ is 2 , then the equation of the tangent to the hyperbola at $(4, 6)$ is (2019 Main, 8 April II)