Question

How do you graph `r=8costheta`?

Answer 1

Explained below

Explanation:

Write the given polar equation as `r^2= 8r cos theta`

Nor convert to cartesean form `r^2= x^2 +y^2` and `r cos theta=x`, so that it is

`x^2 +y^2= 8x`

`x^2 -8x +16-16+y^2=0`

`(x-4)^2 +y^2= 16`

This equation represents a circle with centre at (4,0) and radius 4. This can now be easily graphed

Answer 2

If you convert this equation to Cartesian coordinates, the resulting equation will be a circle.

Explanation:

Given: `r = 8cos(theta)`

Multiply both sides by r:

`r^2 = 8rcos(theta)`

Substitute the Cartesian conversion equations:

`x^2+y^2 = 8x`

Add the `-8x + h^2` to both sides:

`x^2-8x+h^2+y^2 = h^2" [1]"`

From the pattern `(x-h)^2 = x^2-2hx+h^2`, we know that:

`-2hx=-8x`

`h = 4`

This makes the equation [1], become:

`(x-4)^2+(y-0)^2=4^2`

This is a circle with a radius of 4 and a center at the Cartesian point `(4,0)`. Because the y coordinate is the polar point is the same, `(4,0)`

To graph the original equation, set your compass to a radius of 4 and put the center at the polar point `(4,0)`