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.

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