Question

What is the polar equation of the vertical line \(x=5 ?\)

Short answer

Answer: The polar equation of the vertical line with the cartesian equation \(x=5\) is \(r=\frac{5}{cos(\theta)}\).

Step-by-step solution

Write down the cartesian equation of the vertical line

The problem gives us the cartesian equation of the vertical line as: \(x=5\)

Replace the x-coordinate with the polar coordinate

Rewrite the cartesian equation in step 1, using the transformation equation \(x = rcos(\theta)\) We have: \(rcos(\theta)=5\)

Isolate the r-coordinate

To obtain the polar equation, isolate r from the equation in step 2: \(r=\frac{5}{cos(\theta)}\)

Final Polar Equation

The polar equation for the given vertical line is: \(r=\frac{5}{cos(\theta)}\)