Final answer:
The radius of a circle with center at (9,2) and a point on its circumference at (-3,-6) is calculated using the distance formula and is approximately 14.42 units.
Step-by-step explanation:
To find the radius of a circle when given the center and a point on the circumference, we use the distance formula which is derived from the Pythagorean theorem. The center of the given circle is (9,2), and the point on the circle is (-3,-6). To calculate the radius, which is the distance between these two points, you apply the distance formula:
Distance = √((x2 - x1)² + (y2 - y1)²), where (x1,y1) and (x2,y2) are the coordinates of the two points.
Substituting the given coordinates:
Radius = √((-3 - 9)² + (-6 - 2)²) = √((-12)² + (-8)²) = √(144 + 64) = √208 ≈ 14.42
To find the radius of a circle given the center and a point, we can use the distance formula. The distance between the center (9,2) and the given point (-3,-6) is found by taking the square root of the sum of the squared differences of the x and y coordinates. In this case, the distance is √((-3-9)² + (-6-2)²) = √(144 + 64) = √208 = 4√13. Therefore, the radius of the circle is 4√13 units.
So, the radius of the circle is approximately 14.42 units.