Consider a parabola y 2 = 4 x with vertex at A and focus at S . P Q is a chord of the parabola which is normal at point P . If the abscissa and the ordinate of the point P are equal, then the square of the length of the diameter of the circumcircle of triangle P S Q is

Question

Consider a parabola y 2 = 4 x with vertex at A and focus at S . P Q is a chord of the parabola which is normal at point P . If the abscissa and the ordinate of the point P are equal, then the square of the length of the diameter of the circumcircle of triangle P S Q is,

MARKS App · Accepted Answer

t 1 2 = 2 t 1 and t 2 = t 1 - 2 t 1 ∴ t 1 = 2 & t 2 = - 3 So, P 4 , 4 and Q 9 , - 6 Slope of P S = 4 3 Slope of Q S = - 6 8 = - 3 4 ⇒ P S ⊥ Q S ∴ P Q is the diameter of the circle passing through P , S , Q . Hence, the length of the diameter = 25 + 100 = 125 ∴ square of the length of the diameter = 125

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