Find a polar equation for the curve represented by the given cartesian equation. y = 6

Solution:

Given, the cartesian equation is y = 6.

We have to find a polar equation for the curve.

We know the cartesian coordinate of a point P can be (x, y) and the polar coordinates of the same point can be (rcosθ, rsinθ).

Converting cartesian to polar coordinate,

x = r cosθ, y = r sinθ

Put y = 6 in the above expression,

6 = r sinθ

r = 6/sinθ

r = 6 cosecθ

Therefore, the polar equation is r = 6 cosecθ.

Find a polar equation for the curve represented by the given cartesian equation. y = 6

Summary:

The polar equation for the curve represented by the given cartesian equation y = 6 is r = 6cosecθ.