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Question

The locus of the curve whose perametric equations are x=a(1t21+t2) and y=2at1+t2, where t being a parameter is

A
a circle with a radius of a units
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B
a circle passing through origin
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C
pair of lines passsing through (a,a)
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D
pair of lines passsing through (0,0)
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Solution

The correct option is A a circle with a radius of a units
Given, x=a(1t21+t2) and y=2at1+t2
x2+y2=a2((1t2)2+4t2(1+t2)2)
x2+y2=a2
Which represents a circle of radius a units.

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