Determine the equation in standard form of the circle given the
(3, − 2), ℎℎ (4,3).
Answer (2)
(x – 3)² + (y + 2)² = 26
Answer:1. Find the center: The center is the midpoint of the diameter. Using the midpoint formula ((x₁ + x₂)/2, (y₁ + y₂)/2): Center = ((3 + 4)/2, (-2 + 3)/2) = (7/2, 1/2) 2. Find the radius: The radius is half the length of the diameter. First, find the diameter's length using the distance formula: Diameter = √((4 - 3)² + (3 - (-2))²) = √(1² + 5²) = √26 Radius = Diameter / 2 = √26 / 2 3. Write the equation: The standard form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius. (x - 7/2)² + (y - 1/2)² = (√26 / 2)² (x - 7/2)² + (y - 1/2)² = 13/2
