Question

If P = (-4,-3) and Q = (2, 1) are the

Answer 1

Answer:

$(x+1)^2 + (y + 1)^2 = 13$

Step-by-step explanation:

To find the centre of the circle, find the mid - point of PQ :

$Centre =( \frac{x_1+x_2}{2} \ , \ \frac{y_1 + y_2}{2}) = (\frac{-2}{2} \ , \ \frac{-2}{2}) = (-1, -1)$

Diameter = 2 x Radius , To Find the diameter, find distance between P and Q:

$Distance , PQ = \sqrt{(2 - (-4))^2 + (1 -(-3))^2}$

                   $= \sqrt{6^2 + 4^2} = \sqrt{36+ 16} = \sqrt{52} = \sqrt{4 \times 13} = 2 \times \sqrt{13}$

PQ is the diameter , therefore radius :

                                                $r = \frac{1}{2} \times 2 \sqrt{13} = \sqrt{13}$

Equation of a circle :

                              $(x + 1)^2 + (y + 1)^2 = 13$