# What is the equation of the tangent line of #r=6cos(theta-(2pi)/3) # at #theta=(-5pi)/3#?

##### 1 Answer

#### Explanation:

graph{(x^2+y^2+3x-5.2y)(x-1.64-.001y)((x-1.5)^2+(y-2.6)^2-.04)=0 [-13, 13, -6.5, 6.5]}

The equation to the family of circles through the pole r = 0 and

having center at

So, here, the radius a = 3 and

When

So, the point of contact of the tangent is

The equation to the tangent at

As

and for the opposite direction, this is

And so, the equation to the tangent is

rcostheta=1.5

In Cartesian form , this is

x=x_P=1.5.

Note that Cartesian P is