Question

The focal distance of a point on the parabola $y^2=12x$ is $4$. Find the abscissa of this point.

• A. $1$
• B. $-1$
• C. $3$
• D. none of these

Answer 1

The correct option is A $1$

The given parabola is of the form $y^2=4ax$. On comparing, we obtain $4a=12$ i.e., $a=3$.

We know that the focal distance of any point $(x,y)$ on $y^2=4ax$ is $x+a$.

Let the given point on the parabola $y^2=12x$ be $(x,y)$. Then, its focal; length is $x+3$.

Therefore, $x+3=4$

$x=1$

Hence, the abscissa of the given point is 1.