Question

What Went Wrong? A student stated that the center and radius of the graph whose equation is (x + 3)²+ (y - 2)²= 16 are

(3, -2) and 4, respectively. Why is this incorrect?

Short answer

The correct center of the given equation is (-3, 2)

Step-by-step solution

Step 1.  Given information

Here equation of a circle with center and radius is given.

We have to check and explain why this given center is incorrect.

Step 2. Explanation of  finding the correct center and radius 

The standard equation of a circle is ${(x-h)}^2+{(y-k)}^2=r^2,where(h,k)iscenterandristheradius$

Here given equation ${(x+3)}^2+{(y-2)}^2=4$is in the standard form of the equation circle, thus compared to the standard form we can rewrite given equation ${\left(x-(-3)\right)}^2+{\left(y-2\right)}^2=4^2$, hence the center is (-3 ,2) and radius 4. this why the student statement on the center is incorrect.