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.


Similar Questions

Find the value of k for which the point (k-1, k) lies inside the parabola \(y^2\) = 4x.

The length of latus rectum of a parabola, whose focus is (2, 3) and directrix is the line x – 4y + 3 = 0 is

What is the equation of common tangent to the parabola \(y^2\) = 4ax and \(x^2\) = 4ay ?

What is the equation of tangent to the parabola having slope m?

Leave a Comment

Your email address will not be published.