If A and B are the points of intersection of the circle x^2+y^2-8x=0 and the hyperbola x^29- y^24=1 and a point P moves on the line 2x-3y+4=0, then the centroid of △ PAB lies on the line:

Question

Accepted Answer

Correct answer: C. (c) C :x^2+y^2-8x=0H : x^29- y^24=1 By solving x^29- ( 8x-x^24 )=1 4x^2-72x+9x^2=36 ⇒13x^2-72x-36=0 ⇒13x^2-78x+6x-36=0 ⇒13x (x-6 )+6 (x-6 )=0 ⇒x=6 or - 136 neglected ⇒y^2=8 (6 )- (6 )^2 ⇒y= 12So, points A and B are (6 , 12 ) , (6 ,- 12 ) P (h , 2h+43 )Centroid of △ PAB is ( 12+h3 , 2h+49 ) By options this centroid lies on the live 6x-9y=20

$If A and B are the points of intersection of the circle x^{2} + y^{2} - 8 x = 0 and the hyperbola \frac{x ^{2}}{9} - \frac{y ^{2}}{4} = 1 and a point P moves on the line 2 x - 3 y + 4 = 0, then the centroid of △ PAB lies on the line:$

Solution

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