Q.62 - Precalculus Enhanced with Graphing Utilities

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?

Step-by-Step Solution

Answer

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

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 ${(x-h)}^2+{(y-k)}^2=r^2 , where (h, k) is center and r is the radius$

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.