Question

The parametric representation of a parabola is $x=3+r^2$, $y=2r-1$. Its focus is

• A. $(3,-1)$
• B. $(3,0)$
• C. $(4,0)$
• D. $(4,-1)$

Answer 1

The correct option is D $(4,-1)$

$x=3+r^2$ , $y=2r-1$ $\Rightarrow r=\frac{y+1}{2}$

$\Rightarrow x=3+{\left(\frac{y+1}{2}\right)}^2$

$\Rightarrow 4(x-3)=(y+1{)}^2$

$\Rightarrow (y+1{)}^2=4(x-3)$

$\therefore$ focus of parabola is $(4,-1)$