Question

Point A(3,2) is on a circle whose center is C(−2,3). What is the equation of the circle? Graph it.

Answer 1

Answer:

(x+2)² + (y-3)² = 26

The graphic is showed below

Step-by-step explanation:

The circle equation is given by the expression:

(x-a)² +(y-b)² = r²

The point (a,b) represents the center, and r is the radius. So:

(x+2)² + (y-3)² = r²

If the point A (3,2) is on the circle, then we can replace it in the equation to find r:

(3+2)² + (2-3)² = r²

r² = 5² + (-1)²

r² = 25 + 1

r² = 26

So, the circle has radius r = √26, and the equation is:

(x+2)² + (y-3)² = 26

To graph it, we must put the center C(-2,3), then the radius r = √26 and form a circle, like the figure below.