Question

convert x^2 +y^2= a^2 to a polar equation

Answer 1

\(x^2+y^2=a^2\) is the equation of a circle with radius \(a\).

When converting to polar, you have \(x^2+y^2=r^2\), so you get
\[r^2=a^2\]
Since \(r>0\), when you take the square root, you disregard the negative root, leaving you with:
\[r=a\]

Answer 2

but to make it a polar equation don't you have to get rid of the a?

Answer 3

No, \(a\) is just a constant.

Answer 4

okay, thanks!!

Answer 5

how would you do r=theta?

Answer 6

\(r=\sqrt{x^2+y^2}\) and \(\tan\theta=\dfrac{y}{x}\).

Answer 7

make that a rectangular equation

Answer 8

so would it be \[x^{2}+y ^{2}=\frac{ y }{ x }\]

Answer 9

Close, you have \(\tan\theta=\dfrac{y}{x}\), so \(\theta=\arctan\dfrac{y}{x}\).

Answer 10

the first equation is only valid if it's r^2

Answer 11

\[r^2=x^2+y^2~~\Rightarrow~~r=\sqrt{x^2+y^2}\]
disregarding the negative root, since \(r\) is necessarily non-negative.

Answer 12

oh!!! thanks!

Answer 13

you're welcome