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A point on the ellipse, 4 x^2+9 y^2=36 , where the normal is parallel to the line, 4 x-2 y-5=0 , is :

Options

  1. A( 9 5 , 8 5 )
  2. B( 8 5 ,- 9 5 )
  3. C(- 9 5 , 8 5 )
  4. D( 8 5 , 9 5 )

Correct answer

C. (- 9 5 , 8 5 )

Step-by-step solution

Given ellipse is 4 x^2+9 y^2=36 x^2 9 + y^2 4 =1 Normal at the point is parallel to the line 4 x-2 y-5=0 Slope of normal =2 Slope of tangent = -1 2 Point of contact to ellipse x^2 a^2 + y^2 b^2 =1 and line is ( a^2 m a^2 m^2+b^2 , b a^2 m^2+b^2 ) Now, a^2=9, b^2=4 Point = ( -9 5 , 8 5 )

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