If the eccentricity of the standard hyperbola passing through the point (4,6) is 2,

Question:

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-

  1. 2x – y – 2 = 0

  2. 3x – 2y = 0

  3. 2x – 3y + 10 = 0

  4. x – 2y + 8 = 0 


Correct Option: 1

Solution:

Let us Suppose equation of hyperbola is

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

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

passing through $(4,6) \Rightarrow \mathrm{a}^{2}=4, \mathrm{~b}^{2}=12$

$\Rightarrow$ equaiton of tangent

$x-\frac{y}{2}=1$

$\Rightarrow 2 x-y-2=0$

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