Question

Find an equation equivalent to r=5/1+cos0 in rectangular coordinates

Answer 1

$r=\dfrac5{1+\cos\theta}\implies r(1+\cos\theta)=5\implies r+r\cos\theta=5$

In converting between polar and rectangular coordinates, we take

$x^2+y^2=r^2\implies r=\sqrt{x^2+y^2}$

$x=r\cos\theta$

so that the equation becomes

$\sqrt{x^2+y^2}+x=5$

which we can rewrite as

$\sqrt{x^2+y^2}=5-x$

$x^2+y^2=(5-x)^2$

$x^2+y^2=25-10x+x^2$

$\implies\boxed{y^2=25-10x}$

so the answer is C.