Hello i was wondering how do you find the equation of a circle in the form of y =?

Question

I have a problem because when i try to rearrange the equation r^2=x^2+y^2 it comes out to be y=sqrt(x^2-r^2). although graphing this gives me half a circle it is eliptical in shape not circular. So i was wondering if anyone knew what i was doing wrong because my origin is (0,0) so it should work. Thank you

Answer 1

Well you have

x^2 + y^2 = r^2

or

y^2 = r^2 - x^2

Square root both sides

y = ± sqrt [r^2 - x^2]


Everyone always forgets the plus/minus. You need two equations for the whole circle.

Oh, if your graph looks elliptical, that's just because the graphing calculator's viewing window isn't a perfect square, it's slightly rectangular. So usually, the distance between points in the horizontal direction is longer than the distance between points in the vertical direction. So if you graphed a square ( y = 2, y = -2, x = 2, x = -2), it would look rectangular even though it's really a square. So don't worry about it.

Answer 2

When you calculate a square root you must consider both the positive and negative values. So there are two functions for you to graph y = sqrt(x^2-r^2)
AND
y = -sqrt(x^2-r^2)

When you are graphing y, you are graphing functions where there may be more than one for a given equation.

Answer 3

y=sqrt(x^2-r^2) is a one to one function so it can't give more than one value for a given x

the +/- is correct and required to plot correctly.

If you use a graphing calculator remember that your screen is not a square, so if you have the same number tick marks on your x and y axis then your circle will look distorted. You probably;y have a function like zoomsquare that will show and undistorted plot

Answer 4

If your circle comes out as elliptical, then you're just making a mistake in the graph. The formula you have is correct, although as someone else pointed out, you have to remember to take the negative square root as well as the positive one to get the other half of the circle.

Answer 5

The circle C(O,r) O=origin O(x0, y0)
(x-x0)^2+(y-y0)^2=r^2
if you have x^2+y^2=r^2
O(0,0)
y=+ or -sqrt(X^2-r^2)

Answer 6

y=pai r2.