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If PQ and Rs are normal chords of the parabola y^(2) = 8x and the points P,Q,R,S are concyclic, then |
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Answer» tangents at P and R meet on X-axis and `y + t_(2) x - 4t_(2) - 2t_(2)^(3) =0`. Equation of curve through, P,Q,R,S is `(y + t_(1)x -4t_(1)-2t_(1)^(3)) (y + t_(2)x -4t_(2) -2t_(2)^(3)) + lambda (y^(2) - 8x) =0` P,Q,R,S are CONCYCLIC, `t_(1) + t_(2) =0` and `t_(1)t_(2) =1 + lambda`. Thus, point of intersection of tangents i.e., `(at_(1)t_(2),a (t_(1)+t_(2))` lies on X-axis. Slope of `PR = (2)/(t_(1)+t_(2))` Hence, PR is parallel to Y-axis. |
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