What is the equation of the tangent at a specific point of y^2 = 4ax at (0, 0)?

(a) x = 0

(b) x = 1

(c) x = 2

(d) x = 3

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Question is from Calculus Application in division Application of Calculus of Mathematics – Class 12

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Correct answer is (a) x = 0

Explanation: Equation of the given parabola is y^2 = 4ax ……….(1)

Differentiating both side of (1) with respect to x we get,

2y(dy/dx) = 4a

Or dy/dx = 2a/y

Clearly dy/dx does not exist at (0, 0). Hence, the tangent to the parabola (1) at (0, 0) is parallel to y axis.

Again, the tangent passes through (0, 0). Therefore, the required tangent to the parabola (1) at (0, 0) is the y-axis and hence the required equation of the tangent is x = 0.