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JEE Main20203 Sep 2020Evening ShiftMathematicsApplication of DerivativesActual

If the tangent to the curve y = e x at a point c , e c and the normal to the parabola y 2 = 4 x at the point 1 , 2 intersect at the same point on the x - axis, then the value of c is .....

Correct answer

0

Step-by-step solution

For the parabola y 2 = 4 x , a = 1 Let a t 2 ,   2 a t = 1 ,   2 ⇒ t = 1 So, equation of normal is t x + y = 2 a t + a t 3 . ⇒ x + y = 3 intersects x - axis at 3 ,   0 Given curve y = e x ⇒ d y d x = e x So, equation of tangent to the curve at c ,   e c is y - e c = e c x - c . At 3 ,   0 ⇒ 0 - e c = e c 3 - c ⇒ c = 4 .

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