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

1 Answer
sente
Dec 1, 2015

Use the equality #r^2 = x^2 + y^2# to find the converted form
#x^2 + y^2 = 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^2#

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

#r^2 = 81#

Now we can use the above equality to substitute in #x# and #y# to get

#x^2 + y^2 = 81#

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

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