Respuesta :
The general formula for a circle with center (a,b) and radius r is
[tex](x-a)^2 + (y-b)^2 = r^2[/tex]
If we know the center and a point on the circle, the squared radius is given by substituting in the point for x and y.
[tex](x - -3)^2 + (y - 1)^2 = (3 - -3)^2 + (1 - 1)^2[/tex]
Answer:
[tex](x+3)^2 + (y-1)^2 = 36[/tex]
To write the equation of a circle, you need its radius and its center. The center is given, and you can easily derive the radius: it is the distance between the center and any point in the circumference.
In your case, the center is [tex] (-3,1) [/tex], and the point on the circumference is [tex] (3,1) [/tex]. These points are 6 units apart, so the radius is 6.
Now, knowing the center [tex] (k,h) [/tex] and the radius [tex] r [/tex], the equation is
[tex] (x-k)^2+(y-h)^2 = r^2 [/tex]
Plugging your values, you have
[tex] (x-(-3))^2+(y-1)^2 = 6^2 \iff (x+3)^2+(y-1)^2 = 36 [/tex]