A pair of perpendicular straight lines is drawn through the origin forming with the line `2x+3y=6` an isosceles triangle right-angled at the origin. The equation to the line pair is

Options

A. `5x^2-24xy-5y^2=0`
B. `5x^2-26xy-5y^2=0`
C. `5x^2+24xy-5y^2=0`
D. `5x^2+26xy-5y^2=0`

Answer

A

Explanation

Given line is `2x+3y=6 tan45^(@)|(m-((-2)/(3)))/(1+m(-2)/(3))|rArr |1-(2)/(3)m|=|(3m+2)/(2)|`
`rArr 3-2m=+-(3m+2)`

Hence , `m_1=-5,m_2=1//5`
Hence , lines are `y=-5x and y=(x)/(5)`
`therefore 5x^2-24xy-5y^2=0` .