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If is the tangent to the parabola and , then find the value of c.

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answer is D.

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Detailed Solution

Let the equation of the tangent be

, and the equation of the parabola be

.
Differentiating the equation of the tangent with respect to x, we get

As the tangent of the parabola is

, the slope of the parabola is equal to the slope of the tangent.
Question Image

Since the value of a is 2, then
Question Image

We know that,

Substitute the value of x in the equation of the parabola, we get
Question Image

Therefore, the point of contact is

.
From the equation of the tangent, we have

. So,

.
Find the value of c:
Question Image

Hence, the correct option is 4.

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