[tex]r=\dfrac5{1+\cos\theta}\implies r(1+\cos\theta)=5\implies r+r\cos\theta=5[/tex]
In converting between polar and rectangular coordinates, we take
[tex]x^2+y^2=r^2\implies r=\sqrt{x^2+y^2}[/tex]
[tex]x=r\cos\theta[/tex]
so that the equation becomes
[tex]\sqrt{x^2+y^2}+x=5[/tex]
which we can rewrite as
[tex]\sqrt{x^2+y^2}=5-x[/tex]
[tex]x^2+y^2=(5-x)^2[/tex]
[tex]x^2+y^2=25-10x+x^2[/tex]
[tex]\implies\boxed{y^2=25-10x}[/tex]
so the answer is C.
