Find the equation of the circle with centre (-3,8) and radius 7.
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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 Given Values
From the problem statement, we are given that the center of the circle is (−3,8) and the radius is 7. Therefore, we can identify h=−3, k=8, and r=7.
Step 3: Substitute 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−8)2=72.
Step 4: Simplify the Equation
Simplify the expression. The term x−(−3) becomes x+3, and 72 becomes 49. Thus, the equation of the circle is (x+3)2+(y−8)2=49.