AIR MATH

Math Question

Homer wants to identiy the center and radis of the circle defined by the equation \( x^{2}+y^{2}-14 x+ \) \( 2 y-25=0 \). He follows these steps: Sleg 1: \( \left(x^{2}-14 x\right)+\left(y^{2}+2 y\right)=25 \) Slep 2 \( \left(x^{2}-14 x+49\right)+\left(y^{2}+2 y+1\right)=25 \) Slep S. \( (x-7)^{2}+(y+1)^{2}=25 \) Slep 4. The center is \( (7,-1) \), and the radius is 5 . At which step did Homer make a mistake, and what was it? (A) Step 1; he did not apply correctly the addition property of equality. (B) Step 2; he failed to add the new constant terms to both sides of the equation. (C) Step 3; he falled to square both sides of the equation. (D) Step 4; he interpreted the equation incorrectly when finding the location of the center.

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