Given the polar equation $r=6$, which of the following is the corresponding Cartesian equation?

• A. $x^2+y^2=6^2$
• B. $x^2+y^2=6$
• C. $y=6$
• D. $x=6$

Answer: (A)

Verified step by step guidance

1. Recall the relationship between polar and Cartesian coordinates: \(x = r \cos \theta\) and \(y = r \sin \theta\).
2. Given the polar equation \(r = 6\), this means the distance from the origin to any point on the curve is always 6.
3. To convert to Cartesian form, use the identity \(r^2 = x^2 + y^2\) which relates the radius in polar coordinates to \(x\) and \(y\) in Cartesian coordinates.
4. Substitute \(r = 6\) into the identity to get \$6^2 = x^2 + y^2$.
5. Simplify the equation to \(x^2 + y^2 = 36\), which is the Cartesian equation of a circle with radius 6 centered at the origin.