Question

The eccentricity of locus of points $(3h+2,k)$ where $(h,k)$ lies on the circle $x^2+y^2=1$ is:

• A. $\frac{1}{3}$
• B. $\frac{\sqrt{2}}{3}$
• C. $\frac{2\sqrt{2}}{3}$
• D. $\frac{1}{\sqrt{3}}$

Answer 1

Answer: (C)

$\frac{2\sqrt{2}}{3}$

Let $p=3h+2$ and $q=k$
$\Rightarrow h=\frac{p-2}{3}$ and $k=q$
Since $(h,k)$ lies on $x^2+y^2=1$
$\Rightarrow h^2+k^2=1$
$\Rightarrow {\left(\frac{p-2}{3}\right)}^2+q^2=1$
Locus is ${\left(\frac{x-2}{3}\right)}^2+y^2=1$
Which has eccentricity $e=\sqrt{1-\frac{1}{9}}=\frac{2\sqrt{2}}{3}$