Question

The parametric equation of a parabola is $x=t^2+1,y=2t+1$ Then which of the following options are correct ?

• A. Vertex is $(1,1)$
• B. Vertex is $(-1,-1)$
• C. Length of latus rectum of parabola is $8$ units
• D. Length of latus rectum of parabola is $4$ units

Answer 1

Answer: (A), (D)

The correct options are
A Vertex is $(1,1)$
D Length of latus rectum of parabola is $4$ units

On eliminating $t$ from parametric equation, we get equation of parabola.
$x={\left(\frac{y-1}{2}\right)}^2+1$
$(y-1{)}^2=4(x-1)$
$\therefore$ vertex is $(1,1)$ and length of latus rectum $=4$ units