Question

The locus of the point $(\sqrt{(3h+2)},\sqrt{3k})$. If $(h,k)$ lies on $x+y=1$ is

• A. A pair of straight lines
• B. A quarter circle
• C. A parabola
• D. An ellipse

Answer 1

Answer: (B)

A quarter circle

Consider the point
$(x,y)=(\sqrt{3h+2},\sqrt{3k})$
Now $h+k=1$ as $(h,k)$ lies on $x+y=1$

$\Rightarrow k=1-h$
Therefore, $(x,y)=(\sqrt{3h+2},\sqrt{3-3h})$
$\Rightarrow x^2=3h+2$ and $y^2=3-3h$
$\Rightarrow x^2=3h+2$ and $3h=3-y^2$
$\Rightarrow x^2=3-y^2+2$
$\Rightarrow x^2+y^2=5$
This represents the equation of circle.