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A line `ax +by +c = 0` through the point `A(-2,0)` intersects the curve `y^(2)=4a` in P and Q such that `(1)/(AP) +(1)/(AQ) =(1)/(4)` (P,Q are in 1st quadrant). The value of `sqrt(a^(2)+b^(2)+c^(2))` isA. 2B. 4C. 6D. 8 |
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Answer» Correct Answer - B Let `P(-2+r cos theta, r sin theta)`. `rArr r^(2) sin^(2) theta - 4r cos theta +8 =0` `rArr (1)/(AP) + (1)/(AQ) =(1)/(r_(1)) +(1)/(r_(2)) =(1)/(4)` `rArr cos theta =(1)/(2) rArr tan theta = sqrt(3)` So, equation of line is `y -0 = sqrt(3) (x+2)` `rArr sqrt(3) x -y +2sqrt(3) =0` So `sqrt(a^(2)+b^(2)+c^(2)) =4`. |
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