What is the equation of a circle with center (7, -14) and solution point (-1, 1)?

Let us take the standard equation of a circle and fill in the information that we are given.

(x-h)^{ 2 }+ (y-k)^{ 2 }= r^{2}

(x-7)^{2 }+ (y-(-14))^{ 2 }=
r^{2 }

Now, we also know that the circle has a solution point (-1, 1) which means it has to fulfill the above equation so let’s plug in -1 for x and 1 for y.

(-1-7)^{2} + (1+14)^{2 }= r^{2
}

(-8)^{2 }+ (15)^{2 }= r^{2
}→ 289=r^{2 }so 17=r.

Therefore, our equation is

^{ }(x-7)^{2
}+ (y+14)^{2 }= 289.