Home
Class 12
MATHS
A straight line through the point A (-2,...

A straight line through the point A `(-2,-3)` cuts the line `x+3y=0` and `x+y+1=0` at B and C respectively. If AB.AC`=20` then equation of the possible line is

A

`x - y =1`

B

`x - y +1 = 0`

C

`3x -y +3 = 0`

D

`3x -y = 3`

Text Solution

Verified by Experts

The correct Answer is:
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)`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINE

    CENGAGE ENGLISH|Exercise Comprehension Type|3 Videos

  • STATISTICS

    CENGAGE ENGLISH|Exercise Archives|10 Videos

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise ARCHIVES (NUMERICAL VALUE TYPE)|1 Videos

Similar Questions

Explore conceptually related problems

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 is

A straight line through the point (2,2) intersects the lines sqrt(3)x+y=0 and sqrt(3)x-y=0 at the point A and B , respectively. Then find the equation of the line A B so that triangle O A B is equilateral.

A straight line through the point (2,2) intersects the lines sqrt(3)x+y=0 and sqrt(3)x-y=0 at the point A and B , respectively. Then find the equation of the line A B so that triangle O A B is equilateral.

A straight line through origin O meets the lines 3y=10-4x and 8x+6y+5=0 at point A and B respectively. Then , O divides the Segment AB in the ratio.

A straight line through A (-15 -10) meets the lines x-y-1=0 , x+2y=5 and x+3y=7 respectively at A, B and C. If 12/(AB)+40/(AC)=52/(AD) prove that the line passes through the origin.

A line passes through the point of intersection of the line 3x+y+1=0 and 2x-y+3=0 and makes equal intercepts with axes. Then, equation of the line is

A Line through the variable point A(1+k;2k) meets the lines 7x+y-16=0; 5x-y-8=0 and x-5y+8=0 at B;C;D respectively. Prove that AC;AB and AD are in HP.

The straight line passing through the point of intersection of the straight line x+2y-10=0 and 2x+y+5=0 is

Find the equation of the straight line drawn through the point of intersection of the lines x+y=4\ a n d\ 2x-3y=1 and perpendicular to the line cutting off intercepts 5,6 on the axes.

Find the equation of the straight line passing through the point of intersection of the two line x+2y+3=0 and 3x+4y+7=0 and parallel to the straight line y-x=8