Let `P Q R` be a right-angled isosceles triangle, right angled at `P(2,1)dot` If the equation of the line `Q R` is `2x+y=3` , then the equation representing the pair of lines `P Q` and `P R` is `3x^2-3y^2+8x y+20 x+10 y+25=0` `3x^2-3y^2+8x y-20 x-10 y+25=0` `3x^2-3y^2+8x y+10 x+15 y+20=0` `3x^2-3y^2-8x y-15 y-20=0`

Options

A. `3x^(2)-3y^(2)+8xy+20x+10y+25=0`
B. `3x^(2)-3y^(2)+8xy-20x-10y+25=0`
C. `3x^(2)-3y^(2)+8xy+10x+15y+20=0`
D. `3x^(2)-3y^(2)-8xy-10x-15y-20=0`

Answer

B

Explanation

The equation of PQ are PR are given by
`y-1=(-2pm tan45^(@))/(1pm (-2)tan45^(@))(x-2)`
`rArr" "y-1=((-2+1)/(1pm2))(x-2)`
`rArr" "y-1=(-1)/(3)(x-2)and y-1=3(x-2)`
`rArr" "x+3y-5=0 and 3x-y-5=0`
The combined equation of these two lines is
`(x+3y-5)(3x-y-4)=0`
`rArr" "3x^(2)-3y^(2)+8xy-20x-10y+25=0`