Locus of Point on Parabola

Given: Point on parabola \( y^2 = 4a x \) is at distance \( 5a \) from focus \( (a, 0) \).

Distance Equation:

\[ (x - a)^2 + y^2 = 25a^2 \] \[ \Rightarrow (x - a)^2 + 4a x = 25a^2 \] \[ \Rightarrow x^2 + 2a x - 24a^2 = 0 \]

Solving gives: \( x = 4a \), \( y = 4a \)

✅ Final Answer: \( \boxed{(4a,\ 4a)} \)