First slide

Definition of a circle

Question

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

Moderate

A

a straight line
B

an ellipse
C

a parabola
D

none of these

Solution

Let $h = 3 α + 2$ and $k = β$ . Then,
$α = \frac{1}{3} - 2$ and $β = k$
$∵ (x, 15)$ lies on the circle $x^{2} + y^{2} = 1$
$∴ a^{2} + β^{2} = 1 \Rightarrow {(\frac{h - 2}{3})}^{2} + k^{2} = 1$
Hence, locus of $(h, k)$ is $\frac{(x - 2)^{2}}{9} + y^{2} = 1,$ which is an ellipse.

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