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MHT CET202415 May 2024Morning ShiftMathematicsParabolaActual

The equation of the tangent to the parabola y^2=8 x , which is parallel to the line 4 x-y+3=0 is

Options

  1. A2 x-8 y+1=0
  2. B8 x-2 y+1=0
  3. C8 x+2 y+1=0
  4. D2 x-8 y-1=0

Correct answer

B. 8 x-2 y+1=0

Step-by-step solution

y^2=8 x Differentiating w.r.t. x , we get aligned & 2 y ~d y ~d x =8 & ~d y ~d x = 4 y aligned Slope of the line 4 x-y+3=0 is 4 . Since the tangent is parallel to 4 x-y+3=0 , their slopes are equal aligned & 4 y =4 & y=1 aligned When y=1, x= 1 8 Equation of the tangent at ( 1 8 , 1 ) is aligned & y-1=4 (x- 1 8 ) & 2 y-2=8 x-1 & 8 x-2 y+1=0 aligned

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