Question

Convert the rectangular equation to polar form
2x - y =3

Answer 1

`(3)/(2\cos\theta - r\sin\theta)`

Explanation:

The polar coordinate system uses two parameters r and θ where r is the magnitude of the radius of the circle in polar form(also known as the radial coordinate) and θ the angle which the which the radius makes relative to the x=axis

The following equations are used to convert from cartesian coordinate to polar coordinates

`r = √(x^2 + y^2)\\\\\\x = r\cos\theta\\\\y= r\sin\theta\\\\`

Substituting for x and y in terms of r and θ into the equation 2x - 3y = 3 gives

`2x - y = 3\\\\2r\cos\theta - r\sin\theta = 3\\\\r(2\cos\theta - r\sin\theta = 3\\\\r = (3)/(2\cos\theta - r\sin\theta)`