Question

Axis of a parabola lies along $x$-axis. If its vertex and focus are at distances $2$ and $4$ respectively from the origin, on the positive $x$-axis then which of the following points does not lie on it?

• A. $(4,-4)$
• B. $(6,4\sqrt{2})$
• C. $(5,2\sqrt{6})$
• D. $(8,6)$

Answer 1

The correct option is D $(8,6)$

Given :
Vertex is $(2,0)$
Here, $a=2$
Equation of the parabola will be $(y-0{)}^2=4\cdot 2(x-2)$
$\Rightarrow y^2=8(x-2).........\left(1\right)$
All the options satisfy $\left(1\right)$ except option (d).
$\therefore (8,6)$ does not lie on the parabola.