This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's how to find the equation of the circle: Step 1: Write the general equation of a circle with the given center. The standard equation of a circle with center (h, k) and radius r is (x - h)^2 + (y - k)^2 = r^2. Given the center (h, k) = (2, 6), the equation becomes: (x - 2)^2 + (y - 6)^2 = r^2 Step 2: Calculate the radius squared (r^2) using the point the circle passes through. The circle passes through the point (-3, 7). We can substitute these coordinates into the equation from Step 1 to find r^2. (-3 - 2)^2 + (7 - 6)^2 = r^2 (-5)^2 + (1)^2 = r^2 25 + 1 = r^2 r^2 = 26 Step 3: Write the final equation of the circle. Substitute the value of r^2 back into the equation from Step 1. (x - 2)^2 + (y - 6)^2 = 26 The equation of the circle is (x - 2)^2 + (y - 6)^2 = 26. Last free one today — make it count tomorrow, or type /upgrade for unlimited.