Question

Locus of the point $(\sqrt{3h},\sqrt{3k+2})$ if it lies on the line $x-y-1=0$ is a

• A. Straight line
• B. Circle
• C. Parabola
• D. None of these

Answer 1

Answer: (C)

Parabola

Locus of point $(\sqrt{3h},\sqrt{3k+2})$ if it lies on line $x-y-1=0$ is :

$\sqrt{3}h-\sqrt{3k+2}-1=0{(\sqrt{3}h-1)}^2={\left(\sqrt{3k+2}\right)}^2{3k}^2+1-2\sqrt{3}h=3k+2{(h-\frac{1}{\sqrt{3}})}^2=3(k+\frac{2}{9})x^2=3y$

Which is parabola.