Find the center of a circle with the equation: x2+y2−4x+2y−11=0
2 answers:
The standard form for the equation of a circle is
The center of such a circle is the point with coordinates (h, k).
To get your equation into that form, you have to complete the square (twice; once for x and once for y).
Add 11 to both sides so the constant appears on the right. Build in some space to add a couple of numbers, like this:
To complete the square on x, look at the coefficient of x (that's -4), take half of it (that's -2), then square it (that's 4). Add 4 inside the first pair of (). Do the same kind of thing for y -- half of 2 is 1 and 1 squared is 1; add 1 inside the second pair of (). Be sure to add 4 and 1 to the right side, too.
The first three terms factor and the next 3 terms factor.
Match this up with the standard form
The center of the circle is (2, -1).
The center of such a circle is the point with coordinates (h, k).
To get your equation into that form, you have to complete the square (twice; once for x and once for y).
Add 11 to both sides so the constant appears on the right. Build in some space to add a couple of numbers, like this:
To complete the square on x, look at the coefficient of x (that's -4), take half of it (that's -2), then square it (that's 4). Add 4 inside the first pair of (). Do the same kind of thing for y -- half of 2 is 1 and 1 squared is 1; add 1 inside the second pair of (). Be sure to add 4 and 1 to the right side, too.
The first three terms factor and the next 3 terms factor.
Match this up with the standard form
The center of the circle is (2, -1).
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