TS EAMCET · Maths · Parabola
The normal at a point on the parabola \(y^2=4 x\) passes through a point P. Two more normals to this parabola also pass through P. If the centroid of the triangle formed by the feet of these three normals is \(\mathrm{G}(2,0)\), then the abscissa of P is
- A 4
- B -4
- C 5
- D -5
Answer & Solution
Correct Answer
(C) 5
Step-by-step Solution
Detailed explanation
Equation of normal to \(y^2=4x\) passing through P\((h,k)\): \(k = -th + 2t + t^3\) \(t^3 + (2-h)t - k = 0\) Roots \(t_1, t_2, t_3\): \(\sum t_i = t_1+t_2+t_3 = 0\) \(\sum t_i t_j = t_1t_2+t_2t_3+t_3t_1 = 2-h\) Centroid \(\mathrm{G}(2,0)\) of feet \((t_i^2, 2t_i)\):…
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