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

Category: QuestionsWhat is the equation of the tangent at a specific point of y^2 = 4ax at (0, 0)?
Editor">Editor Staff asked 11 months ago

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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1 Answers
Editor">Editor Staff answered 11 months ago

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.