Question

the tangent to the parabola x= y2+c from origin are perpendicular then c is equal to

Answer 1

Answer:

Step-by-step explanation:

Let y=mx is tangent to the parabola y^2 +c=x

So the equation m^2 x^2 −x+c=0 will have equal roots.

b^2-4ac = 1−4cm^2

       0  = 1 - 4 c m^2 => m^2 = 1 / 4 c  

So for perpendicular tangents

m1 x m2 =−1

⇒- 1 / 4c   = -1

​ ⇒   4c   = 1

    c  = 1/4

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