AIR MATH

Math Question

Homer wants to identify the center and radius of the circle defined by the equation \( x^{2}+y^{2}-14 x+ \) \( 2 y-25=0 . \) He follows these steps: Step 1: \( \left(x^{2}-14 x\right)+\left(y^{2}+2 y\right)=25 \) Step 2: \( \left(x^{2}-14 x+49\right)+\left(y^{2}+2 y+1\right)=25 \) Step 3: \( (x-7)^{2}+(y+1)^{2}=25 \) Step 4: The center is \( (7,-1) \), and the radius is 5 . At which step did Homer make a mistake, and what was it?

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