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

Solution :

The given parabola is of form \(y^2\) = 4ax. On comparing, we have 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 \(y^2\) = 12 x be (x, y). Then its focal distance be x + 3.

\(\therefore\) x + 3 = 4 \(\implies\) x = 1.

Hence, the abscissa of the given point is 1.