# If y = mx + 4 is a tangent to the both the parabolas ,y^2 = 4 x and x^2 =2 by then b is equal to ?

Solution :

Any tangent to the parabola y^ 2 = 4x  is y =mx + a/m

comparing it with  y = mx + 4 ,we get  m =1/4

Equation of tangent becomes  y = x/4 + 4

y = x/4 + 4 is a tangent to x^2 = 2by

Now

x^2 = 2b ( x/4 +4)

or  2x^2 - bx  -16b =0

D = 0

b^2 + 128 b = 0

b = - 128 ANS

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