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AP EAMCET202017 Sep 2020Morning ShiftMathematicsParabolaActual

Tangents are drawn to the hyperbola (x^2-9 y^2=9 ) from point ((3,2) ). Then, the area of the triangle formed by the tangents and the chord of contact is ____ sq units.

Options

  1. A10
  2. B6
  3. C12
  4. D8

Correct answer

D. 8

Step-by-step solution

Given hyperbola ( x^2 9 - y^2 1 =1 ) So, (y=m x 9 m^2-1 ) represent tangents which passes through ((3,2) ) ( m= 5 12 ) ( ) Tangents are (12 y=5 x+9 and x=3 ) Chord of contact will be ( x x₁ a^2 - y y₁ b^2 =1 ) ( 3 x 9 - 2 y 1 =1 x-6 y=3 ) The vertices of the triangle formed with tangents and chord will be ((3,2),(3,0) ) and ( (-5,- 4 3 ) ) So, area of ( = 1 2 | array ccc 3 & 2 & 1 3 & 0 & 1 -5 & -4 / 3 & 1 array |=8 ) unit (^2 )

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