Question

Write the equation of the circle:center at (5, - 2) , passes through (4, 0)

Answer 1

the equation of the circle is

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

if we replace the terms

(4-5)^2 + (0-(-2))^2 = r^2

Now, we can fin the radius if we solve the previous equation

( - 1 )^2 + ( 2 )^2 =r^2

1 + 4 = r^2

5 = r^2

r = SQRT(5)

Now, since we already know r, we can replace it in the circle equation to obtain the result

so, (x-h)^2 + (y-k)^2 = r^2

iquals to, (x-5)^2 + (y+2)^2 = 5