This English question involves literary analysis, grammar, or writing skills. The detailed response below provides a well-structured answer with supporting evidence and clear explanations.
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here's the solution for question 12 in English. Question 12: The equation of a circle is given by x^2 + y^2 - 6x + 2y - 6 = 0. Determine the coordinates of the center and the radius of the circle. (4 marks) Step 1: Rearrange the equation to group the x-terms and y-terms, and move the constant to the right side. The given equation is x^2 + y^2 - 6x + 2y - 6 = 0. (x^2 - 6x) + (y^2 + 2y) = 6 Step 2: Complete the square for both the x-terms and the y-terms. To complete the square for x^2 - 6x, take half of the coefficient of x (which is -6/2 = -3) and square it ((-3)^2 = 9). To complete the square for y^2 + 2y, take half of the coefficient of y (which is 2/2 = 1) and square it (1^2 = 1). Add these values to both sides of the equation: (x^2 - 6x + 9) + (y^2 + 2y + 1) = 6 + 9 + 1 (x - 3)^2 + (y + 1)^2 = 16 Step 3: Identify the coordinates of the center and the radius. The standard equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius. Comparing our equation (x - 3)^2 + (y + 1)^2 = 16 with the standard form: The center (h, k) is (3, -1). The radius squared r^2 is 16, so the radius r = sqrt(16) = 4. The coordinates of the center are (3, -1) and the radius is 4 units. Center: (3, -1), Radius: 4 Got more? Send 'em 📸