Answer:
[tex](x+1)^2 + (y + 1)^2 = 13[/tex]
Step-by-step explanation:
To find the centre of the circle, find the mid - point of PQ :
[tex]Centre =( \frac{x_1+x_2}{2} \ , \ \frac{y_1 + y_2}{2}) = (\frac{-2}{2} \ , \ \frac{-2}{2}) = (-1, -1)[/tex]
Diameter = 2 x Radius , To Find the diameter, find distance between P and Q:
[tex]Distance , PQ = \sqrt{(2 - (-4))^2 + (1 -(-3))^2}[/tex]
[tex]= \sqrt{6^2 + 4^2} = \sqrt{36+ 16} = \sqrt{52} = \sqrt{4 \times 13} = 2 \times \sqrt{13}[/tex]
PQ is the diameter , therefore radius :
[tex]r = \frac{1}{2} \times 2 \sqrt{13} = \sqrt{13}[/tex]
Equation of a circle :
[tex](x + 1)^2 + (y + 1)^2 = 13[/tex]
