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KCET2016MathematicsParabola

The length of latus rectum of the parabola ( 4 y²+3 x+3 y+1=0 ) is

Options

  1. A( 4 3 )
  2. B( 07 )
  3. C( 12 )
  4. D( 3 4 )

Correct answer

D. ( 3 4 )

Step-by-step solution

Given parabola [ array l 4 y²+3 x+3 y+1=0 y²+ 3 4 y+ 1 4 = -3 4 x (y+ 3 8 )²- ( 3 8 )²+ 1 4 = -3 4 x (y+ 3 8 )²+ 7 64 = -3 4 x (y+ 3 8 )²=- 3 4 x- 7 64 (y+ 3 8 )²= -3 4 (x+ 7 48 ) (y+ 3 8 )²= -3 4 (x+ 7 48 ) (1) array ] Comparing Eq. (1) with standard equation of parabola, ( y²=4 a X ) Therefore, length of latus rectum is ( 3 4 )

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