A straight line passing through the point `A(-2,-3)` cuts lines `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`

A straight line passing through the point `A(-2,-3)` cuts lines `x +3y

1.	A straight line passing through the point `A(-2,-3)` cuts lines `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`
Answer» Correct Answer - A::C Any point on line through A is `(-2 +r cos theta, -3 +r sin theta)` `:. (-2+AB cos theta, -3 +AB sin theta)` lies on `x +3y = 9` `:. AB = (20)/((cos theta +3 sin theta))`, similarly `AC = (4)/((cos theta + sin theta))` `AB xx AC = 20` `:. 4 = cos^(2) theta +4 sin theta cos theta +3 sin^(2) theta` `:. 4 +4 tan^(2) theta = 1 +4 tan theta +3 tan^(2) theta` `:. tan^(2) theta - 4 tan theta +3 = 0` `:. tan theta = 1` or `tan theta = 3` `:.` Required lines are `y +3 =x +2` or `y +3 =3 (x+2)`

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