A diagonal of the rectangle formed by the lines `x^2-4x+3=0 and y^2-6y+8=0` is given by

Options

A. `x+y=5`
B. `x-y=5`
C. `x+y=8`
D. `x-y=3`

Answer

A

Explanation

Given pain of lies are `x^2-4x+3=0 and y^2-6y+8=0`
`rArr (x-1)(x-3)=0 and (y-2)(y-4)=0`
`rArr "Lies" x=1,x=3 and y=2,y=4`

The intersection point of lines are `A(1,2),B(3,2),C(3,4) and D(1,4)`.
Now , equation of diagonal AC is `y-2=(4-2)/(3-1)(x-1)[because y-y_(1)=(y_2-y_1)/(x_2-x_1)(x-x_1)]`
`rArr y-4=-1(x-1)`
`rArr x+y-5=0` .