Question

Write the standard form equation of each circle based on the provided information.

Center: (-9, -3), Radius: 2
Center: (8, -3), Radius: 9
Center: (-27/2, 15/2), Radius: 4
Center: (5, 9), Radius: 6

Answer 1

The standard form equations for the circles with provided centers and radii are found by using the formula (x - h)^2 + (y - k)^2 = r^2 and plugging in the corresponding values for each circle.

Step-by-step explanation:

The standard form equation for a circle with a center at (h, k) and a radius of r is (x - h)^2 + (y - k)^2 = r^2. Let's write the equations for each given circle:

• For the center (-9, -3) and radius 2, the equation is (x + 9)^2 + (y + 3)^2 = 2^2 which simplifies to (x + 9)^2 + (y + 3)^2 = 4.
• For the center (8, -3) and radius 9, the equation is (x - 8)^2 + (y + 3)^2 = 9^2 which simplifies to (x - 8)^2 + (y + 3)^2 = 81.
• For the center (-27/2, 15/2) and radius 4, the equation is (x + 27/2)^2 + (y - 15/2)^2 = 4^2 which simplifies to (x + 27/2)^2 + (y - 15/2)^2 = 16.
• For the center (5, 9) and radius 6, the equation is (x - 5)^2 + (y - 9)^2 = 6^2 which simplifies to (x - 5)^2 + (y - 9)^2 = 36.