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A straight line through the point A `(-2,-3)` cuts the line `x+3y=9` and `x+y+1=0` at B and C respectively. If AB.AC`=20` then equation of the possible line isA. `x-y=1`B. `x-y+1=0`C. `3x-y+3=0`D. `3x-y=3` |
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Answer» Correct Answer - A::C Any point on line through A is `(-2+rcostheta,-3+rsintheta)` `because(-2+Abcostheta,-3+Absintheta)` liesd on `x+3y=9` `becauseAB=(20)/((costheta+3sintheta))` similarly `AC=(4)/((costheta+sintheta))` `because4=cos^(2)theta+4sinthetacostheta+3sin^(2)theta` `4+4tan^(2)theta=1+4tantheta+3tan^(2)theta` `tan^(2)theta-4tantheta+3=0` `tantheta=1` or `tantheta=3` `implies` required lines are `y+3=x+2` or `y+3=3(x+2)` |
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