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JEE Advanced2010MathematicsStraight LinesActual

Paragraph: Tangents are drawn from the point P(3,4) to the ellipse x^2 9 + y^2 4 =1 touching the ellipse at points A and B . Question: The orthocentre of the triangle P A B is

Options

  1. A(5, 8 7 )
  2. B( 7 5 , 25 8 )
  3. C( 11 5 , 8 5 )
  4. D( 8 25 , 7 5 )

Correct answer

C. ( 11 5 , 8 5 )

Step-by-step solution

Equation of A B is aligned y-0 & = 8 5 - 9 5 -3 (x-3)= 8 -24 (x-3) y & =- 1 3 (x-3) x & +3 y=3 aligned Equation of the straight line perpendicular to A B through P is 3 x-y=5 . Equation of P A is x-3=0 . The equation of straight line perpendicular to P A through B ( -9 5 , 8 5 ) . is y= 8 5 . Hence, the orthocentre is ( 11 5 , 8 5 ) .

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