Find a polar equation for the curve represented by the given cartesian equation. y = 7

Solution:

Given, the cartesian equation is y = 7.

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 = rcosθ

y = rsinθ

Put y = 7 in the above expression,

7 = rsinθ

r = 7/sinθ

r = 7cosecθ

Therefore, the polar equation is r = 7cosecθ.

Find a polar equation for the curve represented by the given cartesian equation. y = 7

Summary:

The polar equation for the curve represented by the given cartesian equation y = 7 is r = 7cosecθ.