Question

How do you convert `x^2 + 5xy + y^2 = 7` to polar form?

Answer 1

`r^2=7/(1+5/2sin2theta)`

Explanation:

To convert from Cartesian to Polar coordinates use the following formulae which link them.

`• x=rcostheta , y=rsintheta`

`rArr r^2cos^2theta+5r^2costhetasintheta+r^2sin^2theta=7`

remove the common factor of `r^2`

`rArrr^2(cos^2theta+5costhetasintheta+sin^2theta)=7`

Simplify using trig. identities

`• sin^2theta+cos^2theta=1" and "`

`• sin2theta=2sinthetacostheta`

`rArrr^2(1+5/2sin2theta)=7`

`rArrr^2=7/(1+5/2sin2theta)`