Question

find an equation of the circle that has center (-2, 6) and passes through (-6, 1).

Explanation:

Step1: Calculate radius squared

Use distance formula: $r^2=(x_2-x_1)^2+(y_2-y_1)^2$. Substitute center $(-2,6)$ and point $(-6,1)$:
$r^2=(-6-(-2))^2+(1-6)^2=(-4)^2+(-5)^2=16+25=41$

Step2: Write circle equation

Standard form: $(x-h)^2+(y-k)^2=r^2$ where $(h,k)=(-2,6)$ and $r^2=41$:
$(x+2)^2+(y-6)^2=41$

Answer:

$(x+2)^2+(y-6)^2=41$