Question

Solve
$(0,0),(-2,1)and$(-3,2)$

Answer 1

Let P(x,y) be the centre of the circle passing through the points o(0,0), A(-2,1) and B(-3,2). Then

,OP=AP=BP

Now, OP=AP

$\Rightarrow {OP}^2={AP}^2$

$\Rightarrow x^2+y^2=({x+2)}^2+({y-1)}^2$

$\Rightarrow x^2+y^2=x^2+y^2+4x-2y+5$

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

and, OP=BP

$\Rightarrow {OP}^2={BP}^2$

$\Rightarrow x^2+y^2=({x+3)}^2+({y-2)}^2$

$\Rightarrow x^2+y^2=x^2+y^2+6x-4y+13$

$\Rightarrow 6x-4y+13=0$
On solving equations (i) and (ii), we get$x=\frac{3}{2}andy=\frac{11}{2}$,
Thus, the cooridinates of the centre are$(\frac{3}{2},\frac{11}{2})$
Now, Radius=$=OP=\sqrt{x^2+y^2}=\sqrt{\frac{9}{4}+\frac{121}{4}}=\frac{1}{2}\sqrt{130}units$