Where did (x-h)^2+(y-k)^2=r^2 even come from? How was it created?
Use of coordinate geometry?
(I know it's the internet and that you can't really show visuals-explain in words?)
Use of coordinate geometry?
(I know it's the internet and that you can't really show visuals-explain in words?)
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The equation of a circle is a consequence of the Pythagorean Theorem.
The circle with radius r and center (h, k) is the set of points (x, y) that are r units away from (h, k).
Consider the right triangle with vertices (h, k), (x, k), and (x, y).
The hypotenuse is the segment connecting (h, k) and (x, y), which has length r.
The horizontal leg is the segment connecting (h, k) and (x, k), which has length |x-h|.
The vertical leg is the segment connecting (x, k) and (x, y), which has length |y-k|.
From the Pythagorean Theorem,
|x-h|^2 + |y-k|^2 = r^2, or equivalently (x-h)^2 + (y-k)^2 = r^2.
Lord bless you today!
The circle with radius r and center (h, k) is the set of points (x, y) that are r units away from (h, k).
Consider the right triangle with vertices (h, k), (x, k), and (x, y).
The hypotenuse is the segment connecting (h, k) and (x, y), which has length r.
The horizontal leg is the segment connecting (h, k) and (x, k), which has length |x-h|.
The vertical leg is the segment connecting (x, k) and (x, y), which has length |y-k|.
From the Pythagorean Theorem,
|x-h|^2 + |y-k|^2 = r^2, or equivalently (x-h)^2 + (y-k)^2 = r^2.
Lord bless you today!
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It is the set of points a distance r from (h,k), using the distance formula.