Determine the standard form of the equation, find the coordinates of the center and the radius of each following circles.
1. (x + 5)2 + (y - 2)2 = 36
2. x2 + (y - 1/4)2 = 16
Answer (1)
Answer:Standard Form of a Circle:The standard form is:(x - h)^2 + (y - k)^2 = r^2(h, k) is the center of the circler is the radius---✅ 1. (x + 5)^2 + (y - 2)^2 = 36➤ Standard form: Already in standard form.We can rewrite:(x - (-5))^2 + (y - 2)^2 = 36➤ Center:(-5, 2)➤ Radius:\sqrt{36} = 6---✅ 2. x^2 + \left(y - \dfrac{1}{4}\right)^2 = 16We can write this as:(x - 0)^2 + \left(y - \frac{1}{4}\right)^2 = 16➤ Standard form: Already in standard form.➤ Center:(0, \frac{1}{4})➤ Radius:\sqrt{16} = 4---✅ Final Answers:Equation Standard Form Center Radius1. Already standard (-5, 2) 62. Already standard (0, ¼) 4
