Question

The coordinates of a moving point $p$ are $(2t^2 + 4, 4t + 6)$. Then its locus will be a

• A. circle
• B. straight line
• C. parabola
• D. ellipse

Answer 1

Answer: (C)

parabola

Answer 2

Let $x=2 t^{2}+4, y=4 t+6$
$\therefore x=2\left(\frac{y - 6}{4}\right)^{2}+4$
$\Rightarrow (y-6)^{2}=8(x-4)$
Hence, it is a locus of parabola.