Question

The distance from the point of intersection of the lines $x^2-y^2-2x+2y=0$ to the point of intersection of the lines $2x^2-5xy+2y^2+x+y-1=0$ is

• A. $1$
• B. $0$
• C. $2$
• D. $4$

Answer 1

The correct option is B $0$

To know the point of intersection in a pair of straight lines we need to partially differentiate once w. r. t. $x$ and then once with respect to $y$ and solve them to get the point. For first line,

1)$\Rightarrow 2x-2=0\Rightarrow x=1$

2)$\Rightarrow -2y+2=0\Rightarrow y=1$

Point $(1,1)$

For second line

1)$\Rightarrow 4x-5y+1=0$

2)$\Rightarrow -5x+4y+1=0$

On solving this, Point$\equiv (1,1)$

Hence they have the same point $(1,1)$

Hence distance =$0$