Home
Class 11
MATHS
Two straight lines u=0a n dv=0 pass thr...

Two straight lines `u=0a n dv=0` pass through the origin and the angle between them is `tan^(-1)(7/9)` . If the ratio of the slope of `v=0` and `u=0` is `9/2` , then their equations are (a) `y+3x=0a n d3y+2x=0` (b)`2y+3x=0a n d3y+2x=0` (c)`2y=3xa n d3y=x` (d) `y=3xa n d3y=2x`

A

y+3x=0 and 3y+2x=0

B

2y+3x=0 and 3y+x=0

C

2y=3x and 3y=0

D

y=3x and 3y=2x

Text Solution

Verified by Experts

Let the slope u=0 be m. Then slope of v=0 is 9m/2. Therefore,
`(7)/(9) = |(m-(9m)/2)/(1+m xx (9m)/(2))| = |(-7m)/(2+9m^(2))|`
`"or " 9m^(2) -9m+2=0 " or " 9m^(2) + 9m +2=0`
`m = (9+-sqrt(81-72))/(18) = (9+-3)/(18) = (2)/(3), (1)/(3)`
`"or " m = (-9+-3)/(18) =- (2)/(3),-(1)/(3)`
Therefore, the equations of the lines are
(i) 3y=x and 2y= 3x
(ii) 3y = 2x and y = 3x
(iii) x+3y = 0 and 3x+2y=0
(iv) 2x+3y=0 and 3x+y =0
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the obtuse angle between the lines x-2y+3=0\ a n d\ 3x+y-1=0.

Find the angles between each of the following pairs of straight line: 3x-y+5=0\ a n d\ x-3y+1=0

Find the acute angle between the lines 2x-y+3=0\ a n d\ x+y+2=0.

Find the angles between each of the following pairs of straight line: 3x+y+12=0\ a n d\ x+2y-1=0

Find the angles between the pairs of straight lines: x+sqrt(3)y-5=0\ a n d\ sqrt(3)x+y-7=0

Find an equation or the line that passes through the point P(2,\ 3,\ 1) and is parallel to the line of intersection o the planes x+2y-3z=4\ a n d\ x-2y+z=0 .

The equation of a straight line passing through the point (2,3) and inclined at an angle of tan^(-1)((1)/(2)) with the line y+2x=5 (a) y=3( b) x=2( c) 3x+4y-18=0 (d) 4x+3y-17=0

A straight line L passes through (3,-2) also inclined at an angle 60^@ to the line sqrt(3x)+y=1.If L also intersects the x-axis, then the equation of L is: (A) y+sqrt(3x)+2-3sqrt3=0 (B) y-sqrt(3x)+2+3sqrt3=0 (C) sqrt(3y)-x+3+2sqrt3=0 (D) sqrt(3y)+x-3+2sqrt3=0

A line passes through (-3,4) and the portion of the line intercepted between the coordinate axes is bisected at the point then equation of line is (A)4x-3y+24=0(B)x-y-7=0(C)3x-4y+25=0 (D) 3x-4y+24=0

If one of the diagonals of a square is along the line x=2y and one of its vertices is (3, 0), then its sides through this vertex are given by the equations (A) y-3x+9=0, 3y+x-3=0 (B) y+3x+9=0, 3y+x-3=0 (C) y-3x+9=0, 3y-x+3=0 (D) y-3x+9=0, 3y+x+9=0