Find the equation of the circle with centre (-2,7) and radius 5.
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Step-by-Step Solution
Step 1: Recall the Standard Equation of a Circle
The standard equation of a circle with center (h,k) and radius r is given by (x−h)2+(y−k)2=r2. This formula is derived from the distance formula, where every point (x,y) on the circle is at 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 (−2,7) and the radius is 5. Therefore, we can identify the values for h, k, and r.
Step 3: Substitute Values into the Equation
Now, substitute the identified values of h=−2, k=7, and r=5 into the standard equation of the circle. Be careful with the double negative for the x -term.
Step 4: Simplify the Equation
Simplify the equation by resolving the double negative and calculating the square of the radius. This gives us the final equation of the circle.