Answer:
[tex](x+4)^2+(y+6)^2=100[/tex]
Step-by-step explanation:
Given a circle centred at the point P(-4,-6) and passing through the point
R(2,2).
To find its equation, we follow these steps.
Step 1: Determine its radius, r using the distance formula
For point P(-4,-6) and R(2,2)
[tex]\text{Distance Formula=}\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\text{Radius=}\sqrt{(2-(-4))^2+(2-(-6))^2} \\=\sqrt{(2+4))^2+(2+6)^2}\\=\sqrt{6^2+8^2}\\=\sqrt{100}\\Radius=10[/tex]
Step 2: Determine the equation
The general form of the equation of a circle passing through point (h,k) with a radius of r is given as: [tex](x-h)^2+(y-k)^2=r^2[/tex]
Centre,(h,k)=P(-4,-6)
r=10
Therefore, the equation of the circle is:
[tex](x-(-4))^2+(y-(-6))^2=10^2\\\\(x+4)^2+(y+6)^2=100[/tex]
