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AP EAMCET2011MathematicsParabola

If a chord of the parabola y^2=4 x passes through its focus and makes an angle with the X -axis, then its length is

Options

  1. A4 ^2
  2. B4 ^2
  3. C4 cosec ^2
  4. D4 ^2

Correct answer

C. 4 cosec ^2

Step-by-step solution

Let P (t^2, 2 t ) be the one end of a focal chord P Q of the parabola y^2=4 x , the coordinate of the other end Q are ( 1 t^2 , -2 t ) . [ t t^ =-1 ] Given, the chord makes a with positive direction of x -axis aligned & = -2 / t-2 t 1 / t^2-t^2 = -2 (1 / t-t) & =(t-1 / t)=2 aligned Now from Eq. (i) aligned P Q & =(t+1 / t)^2 P Q & =(t-1 / t)^2+4 & =(2 )^2+4 & =4 ( ^2 +1 ) & =4 cosec ^2 aligned

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