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KVPY2010MathematicsParabola

A circle touches the parabola y ²=4 x at (1,2) and also touches its directrix. The y -coordinates of the point of contact of the circle and the directrix is-

Options

  1. A2
  2. B2
  3. C2 2
  4. D4

Correct answer

C. 2 2

Step-by-step solution

y²=4 x2 y d y d x =4m_ T = 2 y = 2 2 =1 Circle S + L =0( x +1)²+( y - )²+ ( x +1)=0 ...(1) differentiate array l 2(x+1)+2(y- ) d y d x + =0 x=1, y=2 4+2(2- ) m_ T + =0 =2 -8...(2) array (1,2) satisfies cq. (1) array l 2²+(2- )²+2 =0 ²-4 +8+2(2 -8)=0 ²=8 =2 2 array

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