Question

1. find the equation of the circle with center (-2, 5) and radius 5.

$(x - 5)^2 + (y + 2)^2 = 25$
$(x + 2)^2 - (y - 5)^2 = 25$
$(x - 2)^2 + (y + 5)^2 = 25$
$(x + 2)^2 + (y - 5)^2 = 25$

Explanation:

Step1: Recall circle standard form

The standard equation of a circle is $(x-h)^2 + (y-k)^2 = r^2$, where $(h,k)$ is the center and $r$ is the radius.

Step2: Substitute given values

Given center $(h,k)=(-2,5)$ and radius $r=5$. Substitute into the formula:
$(x-(-2))^2 + (y-5)^2 = 5^2$

Step3: Simplify the expression

Simplify the signs and radius squared:
$(x+2)^2 + (y-5)^2 = 25$

Answer:

$\boldsymbol{(x+2)^2 + (y-5)^2 = 25}$ (corresponding to the fourth option)