Question

For the given rectangular equation give its equivalent polar equation

Answer 1

The last option

`r = (14)/(6\cos\theta - \sin\theta)`

Explanation:

Given equation is 6x - y = 14

To convert an equation in rectangular(cartesian) form, f(x, y) to polar f(r, θ) we use the following information

x = rcosθ

y = rsinθ

Substituting for x and y in the original rectangular equation 6x - y = 14,

6(rcosθ) - rsinθ = 14

Factoring out r on the left side,
r(6cosθ - sinθ) = 14

which gives

`r = (14)/(6\cos\theta - \sin\theta)`

That would be choice 4