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If a point $(α, β)$ lies on the circle $x^{2} + y^{2} = 1$
then the locus of the point ( 3a + 2, P), $(3 α + 2, β),$ is

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a straight line

an ellipse

a parabola

none of these

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detailed solution

Correct option is B

Let h=3α+2 and k=β. Then,α=13−2 and β=k∵ (x,15) lies on the circle x2+y2=1∴ a2+β2=1⇒h−232+k2=1Hence, locus of (h, k) is (x−2)29+y2=1, which is an ellipse.

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If a point (α, β) lies on the circle x2+y2=1then the locus of the point ( 3a + 2, P), (3α+2, β), is

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If a point $(α, β)$ lies on the circle $x^{2} + y^{2} = 1$
then the locus of the point ( 3a + 2, P), $(3 α + 2, β),$ is