Question

There is a parabola having axis as $x$-axis, vertex is at a distance of $2$ unit from origin & focus is at $\left(4,0\right)$.

Which of the following point does not lie on the parabola.

• A. $\left(6,8\right)$
• B. $\left(5,2\sqrt{6}\right)$
• C. $\left(8,4\sqrt{3}\right)$
• D. $\left(4,-4\right)$

Answer 1

The correct option is A

$\left(6,8\right)$

Explanation for the correct answer:

Compute the required point:

The vertex of the parabola is $\left(2,0\right)$.

$a=2$

The equation of the parabola is given as

${\left(y-0\right)}^2=4a\left(x-2\right)$

$y^2=8\left(x-2\right)$

Consider point $A\left(6,8\right)$

Substitute these coordinates in the equation of the parabola. That is

$64=8\left(6-2\right)$

$=8\times 4=32$

$64\ne 32$

As these co-ordinates do not satisfy the equation of the parabola,

The point $\left(6,8\right)$ does not lie on the parabola.

Consider point $B\left(5,2\sqrt{6}\right)$

Substitute these coordinates in the equation of the parabola. That is

$24=8\left(5-2\right)$

$=8\times 3=24$

$24=24$

As these co-ordinates satisfy the equation of the parabola,

The point $\left(5,2\sqrt{6}\right)$ lies on the parabola.

Similarly points $\left(8,4\sqrt{3}\right)$ and $\left(4,-4\right)$ also lie on the parabola

Hence, option $\left(A\right)$ is the correct answer.