Question

Find Cartesian form of equation r=9cos (theta)?

Answer 1

`x^2+y^2-9x=0`

Explanation:

we need the rectangular `rarr`Polar transformations

`r^2=x^2+y^2`

`x=rcostheta`

`y=rsintheta`

we have

`r=9costheta`

multiply by `r`

`r^2=9rcostheta`

using the transformations above

`x^2+y^2=9x`

`x^2+y^2-9x=0`

Answer 2

`x^2-9x+y^2=0`

Explanation:

`"to convert from "color(blue)"polar to cartesian"`

`•color(white)(x)r=sqrt(x^2+y^2)`

`•color(white)(x)x=rcosthetarArrcostheta=x/r`

`r=(9x)/r`

`"multiply through by "r`

`r^2=9x`

`x^2+y^2=9x`

`x^2-9x+y^2=0`

`(x-9/2)^2+y^2=81/4`

`"which is the equation of a circle "`

`"centre "=(9/2,0)," radius "=9/2`