Practice!

Sample Problem

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

 

Solution

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

(x-h) 2 + (y-k) 2 ­= r2

(x-7)2 + (y-(-14)) 2 ­= r2

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 = r2

(-8)2 + (15)2 = r2 → 289=r2 so 17=r.

Therefore, our equation is

 (x-7)2 + (y+14)2 ­= 289.