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AP EAMCET2001MathematicsParabola

If the normal to the parabola y^2=4 x at P(1,2) meets the parabola again in Q , then coordinates of Q are

Options

  1. A(-6,9)
  2. B(9,-6)
  3. C(-9,-6)
  4. D(-6,-9)

Correct answer

B. (9,-6)

Step-by-step solution

The given equation of the parabola is y^2=4 x Equation of tangent at (1,2) is aligned & & y 2 & =2(x+1) & & y & =x+1 aligned Slope of tangent =1 slope of the normal =-1 Equation of the normal passing through (1,2) is aligned & y-2=-1(x-1) & y-2=-x+1 x+y=3 aligned This equation again meet at Q of the parabola, then array cc & y^2=4(3-y) & y^2=12-4 y y^2+4 y-12=0 & (y-2)(y+6)=0 & y=2,6 array If y=-6 , then x=3-(-6)=9 The coordinates of point Q are (9,-6) .

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