Question

The equation of the circle circumscribing a triangle formed by points $(0,0),(1,0)$ and $(0,1)$ is

• A. $x^2+y^2+x+y=0$
• B. $x^2+y^2+x-y+2=0$
• C. $x^2+y^2-x-y=0$
• D. $x^2+y^2-x-y-2=0$

Answer 1

Answer: (C)

$x^2+y^2-x-y=0$

Let equation of circle be $x^2+y^2+ax+by+c=0$

If the circle go to point (0,0)

Then $(0{)}^2+(0){)}^2+(0)a+(0)b+c=0$

$\Rightarrow c=0$.............................................(1)

If the circle go to point (1,0)

Then $(1{)}^2+(0){)}^2+(1)a+(0)b+c=0$

$\Rightarrow 1+a+c=0$.............................................(2)

If the circle go to point (0,1)

Then $(0{)}^2+(1){)}^2+(0)a+(1)b+c=0$

$\Rightarrow 1+b+c=0$.............................................(3)

Then equation from (2) and (1) we get $a=-1$

And equation from (3) and (1) we get $b=-1$

Put the value of a, b, and c we get equation of circle is

$x^2+y^2+(-1)x+(-1)y+0=0$

$\Rightarrow x^2+y^2-x-y=0$