Standard Circle
How do I turn (x^2 + y^2 -4x + 8y - 5 = 0) into standard form for a circle?
My math question asks, "Show that the equation (above) represents a circle. Find coordinates of the center and radius of the circle." I missed the class where we studied circle functions, what do I do?
First, bring all x and y terms together and bring the constant to the RHS.
x^2 - 4x + y^2 + 8y = 5
Now, we complete the squares on BOTH x and y. Giving:
(x^2 - 4x + 4) + (y^2 + 8y + 16) = 5 + 4 + 16 (Make sure to balance!)
==> (x^2 - 4x + 4) + (y^2 + 8y + 16) = 25
Now, the LHS factors to:
(x - 2)^2 + (y + 4)^2 = 25
==> (x - 2)^2 + (y + 4)^2 = 5^2
Comparing this to the general form of a circle gives that the center is (2, -4) and the radius is 5.
I hope this helps!
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