Mathematics

The key here is using the parabola's equation to find where a point with a known $y$-coordinate actually sits. Since $P$ lies on $y^2 = 4ax$ and you know its ordinate (the $y$-value) is $6a$, you can substitute directly into the equation to solve for the $x$-coordinate. This gives you the complete location of point $P$, which is usually the first step toward finding distances, tangent lines, or other geometric properties.

The key here is using the parabola's equation to find where a point with a known $y$-coordinate actually sits. Since $P$ lies on $y^2 = 4ax$ and you know its ordinate (the $y$-value) is $6a$, you can substitute directly into the equation to solve for the $x$-coordinate. This gives you the complete location of point $P$, which is usually the first step toward finding distances, tangent lines, or other geometric properties.