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AP EAMCET202319 May 2023Morning ShiftMathematicsParabolaActual

If the focal chord drawn through the point P (5,5) to the parabola y ^2=5 x meets the parabola again at the point Q , then the tangent drawn to this parabola at Q meets the axis of the parabola at the point

Options

  1. A( -5 4 , 0 )
  2. B( 5 16 , 0 )
  3. C( -5 16 , 0 )
  4. D( 5 4 , 0 )

Correct answer

C. ( -5 16 , 0 )

Step-by-step solution

y^2=5 x focus ( 5 4 , 0 ) Equation of focal chord (y-5)= ( 5-0 5- 5 4 )(x-5) 4 x-3 y=5 Solving y ^2=5 x & 4 x-3 y=5 , we get: Coordinate of Q ( 5 16 ,- 5 4 ) Slope at point Q m= d y d x = S 2 y =-2 Now, the equation of tangent at Q is y+ 5 4 =-2 (x- 5 16 ) y+ 5 4 =-2 x+ 10 8 ... (i) Now, since the axis of parabola is y=0 So, from equation (i), x=- 5 16 The required point is ( 5 16 , 0 )

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