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
To draw the circle, we first need to find its center and radius from the given equation. We will convert the general form of the equation to the standard form (x-h)^2 + (y-k)^2 = r^2 by completing the square. The given equation is: x^2 + y^2 - 4x + 6y + 4 = 0 Step 1: Group the x terms and y terms, and move the constant to the right side of the equation. (x^2 - 4x) + (y^2 + 6y) = -4 Step 2: Complete the square for the x terms. Take half of the coefficient of x (which is -4), square it ((-2)^2 = 4), and add it to both sides. (x^2 - 4x + 4) + (y^2 + 6y) = -4 + 4 Step 3: Complete the square for the y terms. Take half of the coefficient of y (which is 6), square it ((3)^2 = 9), and add it to both sides. (x^2 - 4x + 4) + (y^2 + 6y + 9) = -4 + 4 + 9 Step 4: Rewrite the expressions in parentheses as squared terms and simplify the right side. (x - 2)^2 + (y + 3)^2 = 9 Step 5: Identify the center (h,k) and radius r. Comparing this to the standard form (x-h)^2 + (y-k)^2 = r^2: The center (h,k) is (2, -3). The radius squared r^2 is 9, so the radius r = sqrt(9) = 3. To draw the circle on a grid, you would: 1. Locate the center point at (2, -3). 2. From the center, measure out 3 units in all directions (up, down, left, right) to mark points on the circle. 3. Draw a smooth curve connecting these points to form the circle. The center of the circle is (2, -3) and the radius is 3. Send me the next one 📸