If the chord joining the points P_1 (x_1 ,y_1 ) and P_2 (x_2 ,y_2 ) on the parabola y^2=12x subtends a right angle at the vertex of the parabola, then x_1x_2-y_1y_2 is equal to

Question

Accepted Answer

Correct answer: C. (c) Parabola y^2=12x has 4a=12, so a=3. Parametric points: P_1= (3t_1^2 ,6t_1 ) ,P_2= (3t_2^2 ,6t_2 ). Chord subtends right angle at vertex O (0 ,0 ) : OP_1 OP_2=0. 9t_1^2t_2^2+36t_1t_2=0 ⇒t_1t_2(t_1t_2+4)=0 ⇒t_1t_2=-4. x_1x_2-y_1y_2=9 (t_1t_2 )^2-36 (t_1t_2 ) =9 (16 )-36 (-4 )=144+144=288.

$If the chord joining the points P_{1} (x_{1}, y_{1}) and P_{2} (x_{2}, y_{2}) on the parabola y^{2} = 12 x subtends a right angle at the vertex of the parabola, then x_{1} x_{2} - y_{1} y_{2} is equal to$

Solution

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