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Q.
The focal distance of a point on the parabola $y ^{2}=12 x$ is 4 . What is the abscissa of the point?
Conic Sections
Solution:
Focal distance of a point $\left(x_{1}, y_{1}\right)$ on the parabola is $y ^{2}=4 ax$ is equal to its distance from directrix
$x + a =0$ is $x _{1}+1$
For $y ^{2}=12 x ; a =3$, so $x _{1}+3=4 \Rightarrow x _{1}=1$