Find a Cartesian equation for the curve A r 4 sec B r2 sin

Find a Cartesian equation for the curve.

A. r = 4 sec

B. r^2 sin 2 = 1

Solution

r = 4 sec

tan = y/x

r = sqrt (x2 +y^2)

so sqrt (x2 +y^2) = 4* sqrt(1 + (y/x)^2)

solving we get

x=4

b)r² 2 sin cos =1

2r cos r sin = 1

2xy = 1:

or y = 1/(2x)