Question

Find an equation of the circle:

Answer 1

Answer:

(x - 3)² + (y + 3)² = 9

Step-by-step explanation:

x–y = 6           y = x - 6

y intercept x = 0     y = -6       (0 , -6)

x intercept y = 0     x = 6         (6 , 0)

if circle center is on line x - y = 6 and tangent to both x and Y axis

the distance from center to X axis and Y axis should be equal, it's the mid-point of segment of x intercept and y intercept

center (h , k)     h = (0 + 6) / 2 = 3       k = (0 + (-6)) / 2 = -3

center (3 , -3)      radius = 3

Equation of circle: (x - h)² + (y - k)² = r²     (x - 3)² + (y + 3)² = 9