The equation of a circle is given below. Identify the radius and the center. Then graph the circle.
* +y - 6x- 8y +21 = 0
To identify the radius and center of the circle, we first need to rewrite the equation in standard form, which is (x - h)^2 + (y - k)^2 = r^2 where (h,k) is the center of the circle and r is the radius.
Given equation: +y - 6x - 8y + 21 = 0
Rearranging terms: y - 8y = 6x - 21
Combining like terms: -7y = 6x - 21
Dividing by -7: y = -6/7x + 3
Since the equation is in the form y = mx + b, the center of the circle will be (0, b) which is (0, 3). To find the radius, we calculate the distance from the center to any point on the circle. One common point on the circle that is easy to calculate the distance to the center from is the y-intercept, which is (0, 3).
Plugging in x = 0 into the equation, we get y = 3. The radius is the distance between (0, 3) and (0, 3) which is 0.
Therefore, the center of the circle is (0, 3) and the radius is 0. This means the circle is just a point at the center (0, 3).
Graph of the circle:
The circle is represented by a single point at the coordinates (0, 3).