Find the center radius and intercepts of the circle with the

Find the center, radius, and intercepts of the circle with the given equation and then sketch the graph. 2x^2 + 2y^2 - 4x + 8y + 2 = 0 The center is (Type an ordered pair.)

Solution

2x^2 + 2y^2 - 4x + 8y + 2 = 0

x^2 + y^2 - 2x + 4y + 1 = 0

x^2 - 2x + 1 + y^2 + 4y + 4 - 4 = 0

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

Center = (1, -2)

Radius = 2

x-intercept,

when y = 0,

(x - 1)^2 + (0 + 2)^2 = 4

(x - 1)^2 = 0

x = 1

X-intercept = (1, 0)

y-intercept, when x = 0

(0 - 1)^2 + (y + 2)^2 = 4

(y + 2)^2 = 3

y1 = +(sqrt 3) - 2 and y2 = (-sqrt 3) - 2

y1 = -0.27 and y2 = -3.73

There is two y-intercept

Y1-intercept = (0, -0.27)

Y2-intercept = (0, -3.73)

Comment below if you have any doubt.