Let PQR be a right - angled isosceles triangle , right angled at P(2,1). If the equation of the line QR is `2x+y=3`, then the equation representing the pair of lines PQ and PR is

Options

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

Answer

2

Explanation

Let m be the slope of PQ . Then ,
`tan45^(@)=|(m-(-2))/(1+m(-2))|=|(m+2)/(1-2m)|`
`:. m+2=1-2mor-1+2m=m+2`
`:. m=-(1)/(3)orm=3`
Hence , the equation of PQ is
`y-1=-(1)/(3)(x-2)`
or `x+3y-5=0` and the equation of PR is
`y-1=3(x-2)`
or `3x-y-5=0`
Hence , the combined equation of PQ and PR is
`(x+3y-5)(3x-y-5)=0`
or ` 3x^(2)-3y^(2)+8xy-20x-10y+25=0`