Find the equation of the circle with centre (−3,2) and radius 4.
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Step-by-Step Solution
Step 1: Recall the standard equation of a circle
The standard equation of a circle is given by (x−h)2+(y−k)2=r2, where (h,k) represents the coordinates of the center of the circle and r represents its radius.
Step 2: Identify the given values
From the problem statement, we are given that the center of the circle is (−3,2) and the radius is 4. Therefore, we can identify h=−3, k=2, and r=4.
Step 3: Substitute the values into the equation
Now, substitute the identified values of h, k, and r into the standard equation of the circle. This gives us (x−(−3))2+(y−2)2=42.
Step 4: Simplify the equation
Simplify the expression by changing x−(−3) to x+3 and calculating 42 which is 16. This yields the final equation of the circle.