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
(b) Step 1: Recall the general equation of a circle. The general equation of a circle is given by x^2 + y^2 + Dx + Ey + F = 0. The center of the circle (h, k) can be found using the formulas h = -(D)/(2) and k = -(E)/(2). Step 2: Identify the coefficients from the given equation. The given equation is x^2 + y^2 + 8x - 6y - 9 = 0. Comparing this to the general form, we have D = 8 and E = -6. Step 3: Calculate the coordinates of the center. Substitute the values of D and E into the formulas for h and k: h = -(8)/(2) = -4 k = -(-6)/(2) = 3 Thus, the center of the circle is (-4, 3). Step 4: Match the result with the given options. The calculated center (-4, 3) corresponds to option (b). The center of the circle is (-4, 3). Send me the next one 📸