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

Options

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

Answer

A, B, C, D

Explanation

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