How do you convert r= 9r=9 into cartesian form?

1 Answer
sente
Dec 1, 2015

Use the equality r^2 = x^2 + y^2r2=x2+y2 to find the converted form
x^2 + y^2 = 81x2+y2=81

Explanation:

The question How do you convert rectangular coordinates to polar coordinates? has a list of equations used when converting between polar and rectangular systems along with their derivations.

For this problem, we will be using
r^2 = x^2 + y^2r2=x2+y2

If we square both sides of the of r = 9r=9 we get

r^2 = 81r2=81

Now we can use the above equality to substitute in xx and yy to get

x^2 + y^2 = 81x2+y2=81

Note that this should make sense intuitively, as r=9r=9 in polar coordinates is all points of distance 99 from the origin, that is, a circle of radius 99 centered at the origin, and the formula for a circle of radius ss centered at (h, k)(h,k) in Cartesian coordinates is (x-h)^2 + (y-k)^2 = s^2(x−h)2+(y−k)2=s2.
Thus a circle of radius 99 centered at the origin would have the formula (x-0)^2 + (y-0)^2 = 9^2(x−0)2+(y−0)2=92

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