Question

Find the equation of a circle with a center at (7,2) and a point on the circle at (-2,-5)

Answer 1

Answer:

(x−7)2+(y−2)2=130

Step-by-step explanation:

The standard form of a circle is

(x-h)^2+(y-k)^2=r^2(x−h)2+(y−k)2=r2

where x and y are points on the circle, h and k are the center, and r is the radius.  We have what we need to fill in everything but the radius, but we will solve for that like this:

(-2-7)^2+(-5-2)^2=r^2(−2−7)2+(−5−2)2=r2

Simplifying gives you

(-9)^2+(-7)^2=r^2(−9)2+(−7)2=r2

and

81+49=r^281+49=r2

so r^2=130r2=130