Rewrite the Cartesian equation y6x2 as a polar equationSolut

Rewrite the Cartesian equation y=6x^2 as a polar equation

Solution

As we know that

x= rcos()

y = r sin()

Now

y = 6x^2

plug above x= rcos() and y = r sin()

r*sin()=6*r^2*cos^2()

divide by r

sin()=6*r*cos^2()

divide by cos^2(x)

sin() / cos^2()=6*r

divide by 6

r= sin() / (6*cos^2())

another equivalent form is:

1/6*tan(x)sec(x)

It is required polar equation