Question

How do you convert `r = 3(4cos(t))` into rectangular form?

Answer 1

`x^2+y^2=12x`

Explanation:

The relation between polar coordinates `(r,t)` and Cartesian coordinates `(x,y)` is given by

`x=rcost`, `y=rsint` and `r^2=x^2+y^2`

Hence, `r=3(4cost)hArrr^2=12rcost` or `x^2+y^2=12x`

i.e. `(x^2-12x+36)+(y-0)^2=6^2`

or `(x-6)^2+(y-0)^2=6^2`

which is nothing but a circle with center at `(6,0)` and radius `6`, whose graph is as follows:
graph{x^2+y^2=12x [-16, 16, -8, 8]}