Question

The circumcentre of the triangle formed by the lines, $xy+2x+2y+4=0$ and $x+y+2=0$ is

• A. $(-1,-1)$
• B. $(-2,-2)$
• C. $(0,0)$
• D. $(-1,-2)$

Answer 1

Answer: (B)

$(-2,-2)$

1. 1) As the given equation of lines,

$xy+2x+2y+4=0$,----------(1)

$x+y+2=0$-----------(2)

on solving eq (1),we get

$x\times (x+2)+2\times (y+2)=0$

$(x+2)\times (y+2)=0$-------(3)

so here equation of three line ar obtained which is as follows,

$X+Y+2=0$,

$X+2=0$ ,and

$Y+2=0$

these lines form a triangle as shown in figure .

Concept of circumcentre:-The circumcentre of a triangle is the point of intersection of the perpendicular bisectors of the side of triangle.

Acc to given equations , triangle ABC will form as shown in the figure

These equations will form a right angle triangle so, circumcentre will be at mid point of BC so, circumcentre is (-2,-2)