Answer:
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