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. $(8,6)$
• D. $(5,2\sqrt{6})$

Answer 1

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

According to the given information, we have the following figure.



Now, if the origin is shifted to $(2,0)$ and $(X,Y)$ is the point with respect to the new origin, then equation of the parabola is
$Y^2=4aX$
where,
$X=x-2$ and $Y=y$ and distance between focus and vertex is $a=4-2=2$

$\therefore$ equation of the parabola is $y^2=8(x-2)$
Now, putting the options in this equation we find that $(8,6)$ is the only point which does not satisfy the equation.