The locus of the curve whose perametric equations are x=a(1−t21+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(1−t21+t2) and y=2at1+t2 ⇒x2+y2=a2((1−t2)2+4t2(1+t2)2) ∴x2+y2=a2 Which represents a circle of radius a units.