The circle below is centered at (2, 3) and has a radius of 4. what is its equation?

The equation is x² + y² - 2x - 3y - 3 =0

Step-by-step explanation:

To find the equation of a circle centered at ( 2,3 ) and having a radius of 4, all we simply do is to use the equation of a circle formula and then simplify,

Equation of a circle : (x - a)² + (y-b)² = r²

where (a,b) are the points at the center of the circle and r is the radius.

In the question given to us, point a and b are 2 and 3 respectively and our radius r=4, so all we need to do is to plug in these values into our equation;

(x - 2)² + (y-3)² = 4²

Now we will open the bracket and then simplify

x² - 2x + 4 + y² - 3y + 9 = 16

we can rearrange this equation;

x² + y² - 2x - 3y + 4 + 9 = 16

x² + y² - 2x - 3y + 13= 16

subtract 16 from both-side of the equation;

x² + y² - 2x - 3y + 13 - 16= 16 - 16

x² + y² - 2x - 3y - 3 = 0

Therefore, the equation of the circle is; x² + y² - 2x - 3y - 3 = 0

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