Question

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

A. x^2=25-10y
B. X^2=10y-25
C.y^2=10x-25
C. Y^2= 25-10x

Answer 1

`r=\frac5{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=√(x^2+y^2)`

`x=r\cos\theta`

so that the equation becomes

`√(x^2+y^2)+x=5`

which we can rewrite as

`√(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.