Question

A circle has its center at (1,4) and a radius of 2 units what is the equation of the circle

Answer 1

The unsimplified answer to the smart person above (the answer to the test) is

(x-1)^2+(y-4)^2=4

Answer 2

Answer: x² + y² - 2x - 8y + 13 = 0

Step-by-step explanation:

the equation of the circle is in the form (x - a)² + (y - b)² = r²

where (a,b) is the center of the circle and r is the radius

      hence the equation is

                         (x - 1)² + (y - 4)² = 2²

                         x²-2x+1+y²-8y+16= 4

                         x²+ y² -2x- 8y + 17 =4

                         x² + y² - 2x - 8y = -13

                          x² + y² - 2x - 8y + 13 = 0