Find the equation of the circle with centre (-5,4) and radius 6.
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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 (−5,4) and the radius is 6. Therefore, we can identify h=−5, k=4, and r=6.
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−(−5))2+(y−4)2=62.
Step 4: Simplify the Equation
Simplify the expression. Subtracting a negative number is equivalent to adding a positive number, so (x−(−5)) becomes (x+5). Also, calculate 62, which is 36.