What is the standard form of the equation of the circle x2 -4x + y2 + 6y + 12 = 0?
1 answer:
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=4
Our goal here is to somehow "surgically remove" the repeating part of the number, so let's start by putting the original value in a variable and messing around with it a bit.
We'll let . We want to cut the
bit off completely, so let's create the scalpel that'll let us do that. If
, then we can also say that
. Maybe I was lying a bit: the
is our real scalpel here, and
is where we'll be making the cut. Mathematically, a "cut" is almost always shorthand for subtraction, so let's see what our operation (cutting
off of
) leaves us with:
The operation was a success! We can now simply divide either side by 9 to find , which, when reduced by dividing the numerator and denominator by 3, gives us