1. Add 25 to both sides of the equation and collect as follows:
x^2 + 10x + 25 + y^2 - 4y - 20 = 25. This can be written as:
(x + 5)^2 + y^2 - 4y - 20 = 25
Now add 4 to both sides and collect as follows:
(x + 5)^2 + y ^2 - 4y + 4 - 20 = 29. This can be written as:
(x + 5)^2 + (y - 2)^2 - 20 = 29
Add 20 to both sides:
(x + 5)^2 + (y - 2)^2 = 49
Now the standard form is (x - xc)^2 + (y - yc)^2 = r^2 where (xc, yc) are the coordinates of the centre and r is the radius.
So we have a circle with centre (-5, 2) and radius 7 (because 7^2 = 49)
2. You can now use the same approach here. To complete the square for the x values add the square of half the coefficient of the x term to both sides (similarly for completing the square of the y terms).
