Question

One of the points on the parabola $y^2=12x$ with focal distance $4$ is

• A. $(3,6)$
• B. $(9,6\sqrt{3})$
• C. $(7,2\sqrt{21})$
• D. $(8,4\sqrt{6})$

Answer 1

The correct option is A

$(3,6)$

Explanation for the correct option

Checking which point lies on the parabola

Given: The parabola is $y^2=12x$ and focal distance $4$

Comparing this with the general equation of the parabola $y^2=4ax$ ,then;

$$\begin{gathered} 4a=12 \\ a=3 \end{gathered}$$

We can say the points lie on point of intersection of the latus rectum and the parabola.So we put $x=3$.

Substituting $x=3$ in $y^2=12x$,we get ;

$$\begin{gathered} y^2=12\times 3 \\ {y}^2=36 \\ y=\sqrt{36} \\ \therefore y=6 \end{gathered}$$

Therefore, the point $(3,6)$lies on the parabola.

Hence the correct answer is Option (A).