Question

question 13 of 25
this circle is centered at the point (3, 2), and the length of its radius is 5. what
is the equation of the circle?

a. $(x - 3)^2+(y - 2)^2 = 25$
b. $(x - 2)^2+(y - 3)^2 = 25$
c. $(x^2 - 3)+(y^2 - 2)=5^2$
d. $(x + 3)^2+(y + 2)^2 = 5$

Explanation:

Step1: Recall the standard form of a circle's equation

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

Step2: Identify the center and radius

Given the center \((h,k)=(3,2)\) and radius \(r = 5\).

Step3: Substitute into the standard form

Substitute \(h = 3\), \(k = 2\), and \(r = 5\) (so \(r^2=25\)) into \((x - h)^2+(y - k)^2=r^2\). We get \((x - 3)^2+(y - 2)^2=25\).

Answer:

A. \((x - 3)^2+(y - 2)^2 = 25\)