The equation of a circle is given below. Identify the radius and the center. Then graph the circle.
x+3-28+6y=15
To identify the radius and center of the circle, we need to rewrite the equation in standard form (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.
Given equation: x^2 + 6x + 9 + y^2 - 28y + 49 = 15
Rearrange terms: x^2 + 6x + y^2 - 28y + 43 = 0
Complete the square for x and y terms:
(x + 3)^2 - 9 + (y - 14)^2 - 196 + 43 = 0
(x + 3)^2 + (y - 14)^2 = 162
Now we can see that the center of the circle is at (-3, 14) and the radius is the square root of 162, approximately equal to 12.73.
To graph the circle, plot the center at (-3, 14) and draw a circle with a radius of approximately 12.73. The circle should be centered at (-3, 14) and extend approximately 12.73 units in all directions.