JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \( y^{2}=12x \) be the parabola with its vertex at O. Let P be a point on the parabola and A be a point on the x-axis such that \( \angle OPA=90^{\circ} \). Then the locus of the centroid of such triangles OPA is :
- A \( y^{2}-6x+4=0 \)
- B \( y^{2}-9x+6=0 \)
- C \( y^{2}-2x+8=0 \)
- D \( y^{2}-4x+8=0 \)
Answer & Solution
Correct Answer
(C) \( y^{2}-2x+8=0 \)
Step-by-step Solution
Detailed explanation
\( m_{Ap}=\frac{-t}{2} \) Equation of AP is \( y-6t=\frac{-t}{2}(x-3t^{2}) \) Put \( y=0\Rightarrow x=12+3t^{2} \) \( \Rightarrow A(12+3t^{2},0) \) Let centroid of \(\Delta\) OPA be \( G(h,k) \) \( \Rightarrow3h=0+3t^{2}+12+3t^{2} \) \( 3k=0+6t+0 \)…
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