Homer has made mistake in step 2
When you complete the square, you need to add the values to both sides of equation
Solution:
Given equation of circle:
[tex]x^2 + y^2 -14x + 2y -25 = 0[/tex]
Let us first calculate center and radius and find out where he did the mistake
Step 1:
Group the terms
[tex]x^2 -14x + y^2 + 2y = 25\\\\(x^2 -14x) + (y^2 + 2y) = 25[/tex]
Step 2:
[tex](x^2 -14x + 49) + (y^2 + 2y + 1) = 25 + 49 + 1[/tex]
But homers step 2 is:
[tex](x^2 -14x + 49) + (y^2 + 2y + 1) = 25[/tex]
So homer has made mistake in this step
When you complete the square, you need to add the values to both sides of equation
But homer did not add 49 and 1 to right side of equation
Correct steps are:
[tex](x^2 -14x + 49) + (y^2 + 2y + 1) = 75\\\\(x-7)^2 + (y+1)^2 = 75[/tex]
Comparing general equation of circle,
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
Therefore, center is ( 7, -1) and radius is 8.66
