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Question

Match the following equation of parabola

Parabolaparametric equationN)x2=4ay1)(at2,2at)E)y2=4ax2)(−at,2at)W)y2=−4ax3)(2at,at2)S)x2=−4ay4)(2at,at2)


A

N-2, E-3, W-1, S - 4

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B

N-1, E-3, W-2, S - 4

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C

N-4, E-1, W-2, S - 3

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D

N-3, E-1, W-2, S - 4

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Solution

The correct option is D

N-3, E-1, W-2, S - 4


The requirements of a parametric representation are it should be able to represent every point on the curve and it should also satisfy the equation of the curve.

But we usually take (at2, 2at) for y2 = 4ax. In our question, we will just substitute and check if it satisfy any equation.

But we need to remember these parametric representation as it will be used later. After substituting and checking we get it as

y2 = 4ax (at2, 2at)

x2= 4ay (2at, at2)

y2 = 4ax (at2, 2at)

x2 = 4ay (2at, at2)


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