Question

The distance of a point $P$ on the parabola ${\mathrm{y}}^2=12\mathrm{x}$, if the ordinate of $P$ is $6$, is

• A. $12$
• B. $6$
• C. $3$
• D. $9$

Answer 1

The correct option is B

$6$

Explanation for the correct option:

Finding the distance:

Given, of the parabola is ${\mathrm{y}}^2=12\mathrm{x}\dots \dots \left(1\right)$

This equation is of the format ${\mathrm{y}}^2=4\mathrm{ax}\dots \dots \left(2\right)$

Rewriting equation $\left(i\right)$, we get

${\mathrm{y}}^2=4\times 3\times \mathrm{x}$

Comparing equations $\left(1\right)\text{and}\left(2\right)$ we get $a=3$

For point $P\left(x,y\right)=6$

Implying the value of P in $\left(1\right)$

$$\begin{gathered} \Rightarrow 6^2=12\mathrm{x} \\ \Rightarrow 36=12\mathrm{x} \\ \Rightarrow \mathrm{x}=3 \end{gathered}$$

Distance of a point on a Parabola is distance between that and its opposite point $(-3,0)$ in this case.

$\Rightarrow$ Distance between $(-3)$ and $(3,0)$

$\Rightarrow \mathrm{D}=6$

Hence, option (B) is the correct option.