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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
A point P in the first quadrant, lies on $y^2 = 4ax$, a > 0, and keeps a distance of 5a units from its focus. Which of the following points lies on the locus of P?
Solution
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: \( \boxed{(4a,\ 4a)} \)
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