Question

Convert the equation 6x+5y+6=0 to polar form?

Answer 1

`r= -6/(6costheta+5sintheta)`

Explanation:

`6x+5y+6=0`

The conversion from Rectangular to Polar:
`x=rcostheta`
`y=rsintheta`

1. Substitute and solve for `r`
   `6(rcostheta)+5(rsintheta)+6= 0`

2. Simplify and factor out `r`
   `6rcostheta+5rsintheta+6= 0`
   `6rcostheta+5rsintheta= -6`
   `r(6costheta+5sintheta)= -6`

3. Solve for `r`
   `r= -6/(6costheta+5sintheta)`