What is the correlation between a circle graphed on a cartesian plane and the formula (x-a)²+(y-b)²=r²? In other words, how did they come up with the previous formula to graph a circle? How does this work?
2007-01-18 06:18:37 · 7 answers · asked by TPCAN 3 in Science & Mathematics ➔ Mathematics
It's basically an extension of the Pythagorean theorem. If you draw a circle, draw any radius, and drop a perpendicular from the point of intersection of that radius to the y-value line passing through the center, you have a right triangle, with the radius as the hypotenuse and x-a and y-b as the two sides.
2007-01-18 06:25:37 · answer #1 · answered by Anonymous · 1⤊ 0⤋
Ok so this is how I see it... A bar graph is best used when you are making a few comparisons with specific numerical values. However, a bar graph becomes a bit cumbersome if you have too many values or are making too many comparisons. Ex. Max Height of a peach tree vs Max Height of Apple tree, etc. A line graph is best used when comparing a lot of data points. Line graphs are wonderful in showing changes over time. Ex. Changes in height of a peach tree from 2000 to 2009 A pie graph ( circle graph) is the easiest in that each slice represents a piece of the whole. So if your messing with a percentage than Pie Graph is best. Ex. A portion of a total amount of peaches given to various individuals. Hope this helps a little. You get the feel for it the more you work with the various graphs.
2016-05-24 03:56:22 · answer #2 · answered by Anonymous · 0⤊ 0⤋
I'm not sure what you mean when you say previous formula. You only have one and to graph that equation, the center of the circle is (a,b) and the radius is r.
2007-01-18 06:26:02 · answer #3 · answered by Gene 7 · 0⤊ 0⤋
The circle is defined as the set or points at a distance r from a center point. If you choose (a,b) as the center, you can form a right triangle from the points (a,b), (x,b), (x,y) [or (a,b), (a,y), (x,y)]. The lengths of the sides are x-a and y-b. By Pythagorean theorem, the hypotenuse of that triangle has length r if it satisfies the condition:
(x-a)²+(y-b)²=r²
The circle is the set of all solutions to the equation.
2007-01-18 06:32:58 · answer #4 · answered by novangelis 7 · 0⤊ 0⤋
Draw a cicle with center at (0,0).
Then pick any point on the circle P(x,y).
Draw a radius r to P(x,y).
It should be obvious to you that x^2+y^2 = r^. This is the equation for a circle wth center at (0,0)
To move the center to some other point (h,k), simply replace x with x-h and y with y-k giving you (x-a)²+(y-b)²=r²
2007-01-18 06:40:01 · answer #5 · answered by ironduke8159 7 · 0⤊ 0⤋
Let (x,y) be a point of the circle,(a,b) the center and r the radius,
The distance squared of (x,y) to (a,b) is (x-a)^2 +(y-b)^2 which should be equal to the radius squared.
So you come up with yout formula
2007-01-18 06:28:37 · answer #6 · answered by santmann2002 7 · 0⤊ 0⤋
In your equation, the center is at (a,b) and the radius is r.
2007-01-18 06:27:43 · answer #7 · answered by davidosterberg1 6 · 0⤊ 0⤋