Find the equation of the circle with centre (-3,2) and radius 8.
Get the complete, step-by-step math solution for: "Find the equation of the circle with centre (-3,2) and radius 8.". Powered by SolveForX AI math tutor.
Step-by-Step Solution
Step 1: Standard Equation of a Circle
The standard equation of a circle with center (h, k) and radius r is given by this formula. This formula is derived from the distance formula, representing all points (x, y) that are a fixed distance r from the center (h, k).
Step 2: Identify Given Values
From the problem statement, we are given that the center of the circle is (−3,2) and the radius is 8. We identify these values as h=−3, k=2, and r=8.
Step 3: Substitute Values into the Equation
Now, we substitute the identified values of h, k, and r into the standard equation of the circle. This step directly applies the given information to the general formula.
Step 4: Simplify the Equation
We simplify the equation. The term (x−(−3)) becomes (x+3), and 82 simplifies to 64. This simplified form is the final equation of the circle.