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)

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