Question

could you help me out with a question

Answer 1

The correct answer is

$(x+4)^2+(y+1)^2=20$

Step1: Find the radius of the circle, using the formula;

$r^2=(x_2-x_1)^2+(y_2-y_1)^2$

$\begin{gathered} O(-4,-1)\Rightarrow x_1=-4;y_1=-1 \\ P(-2,3)\Rightarrow x_2=-2;y_2=3 \\ r^2=|OP|^2=(-2--4)^2+(3--1)^2 \\ r^2=(-2+4)^2+(3+1)^2 \\ r^2=2^2+4^2=4+16=20 \end{gathered}$

The equation of the circle is

$\begin{gathered} (x--4)^2+(y--1)^2=r^2 \\ (x+4)^2+(y+1)^2=20 \end{gathered}$