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 \left ( 4,6 \right ) is  :

  • Option 1)

    x-2y+8=0

  • Option 2)

    2x-3y+10=0

  • Option 3)

    2x-y-2=0

     

  • Option 4)

    3x-2y=0

 

Answers (1)


Standard equation of hyperbola 

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

passes via point \left ( 4,6 \right )

\frac{16}{a^{2}}-\frac{36}{b^{2}}=1\cdots (1)

Also, given eccentricit = 2

e^{2}=1+\frac{b^{2}}{a^{2}}=4

a^{2}=4\: \: ,\: \: b^{2}=12

Equation of tangent.

\frac{xx_1}{a^{2}}-\frac{yy_1}{b^{2}}=1

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

2x-y-2=0


Option 1)

x-2y+8=0

Option 2)

2x-3y+10=0

Option 3)

2x-y-2=0

 

Option 4)

3x-2y=0

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