How do you convert r = 4 cosθ + 4 sinθ into a cartesian equation?

Question

8673 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-18T17:01:00

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

We know that $x=rcostheta$ and $y=rsintheta$

$rArr x/r =costheta$ and $y/r=sintheta$

Put the above values in the equation :-

$r=4costheta +4sintheta$

$rArrr=(4(x+y))/r$

$rArrr^2=4(x+y)$

Also we know that $x^2+y^2=r^2$ ; put in the equation we get :-

$rArrx^2+y^2=4(x+y)$

$:.x^2+y^2-4(x+y)=0$ which is the cartesian form of the given equation.