Question

transform the polar equation to an equation in rectangular coordinates. then identify and graph the equation
r = 6

what is the standard form of the equation in rectangular form?

Explanation:

Step1: Recall the relationship between polar and rectangular coordinates

We know that \(x = r\cos\theta\), \(y = r\sin\theta\), and \(r^{2}=x^{2}+y^{2}\)

Step2: Square both sides of the given polar equation

Given \(r = 6\), squaring both sides gives \(r^{2}=36\)

Step3: Substitute \(r^{2}=x^{2}+y^{2}\)

Since \(r^{2}=x^{2}+y^{2}\), the equation in rectangular coordinates is \(x^{2}+y^{2}=36\)

Answer:

\(x^{2}+y^{2}=36\)