I've been working on this problem for hours, still don't know how to do it.
Directions: convert from polar to rectangular equation.
Directions: convert from polar to rectangular equation.
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r = 2/(1 - secΘ) ==> r(1 - secΘ) = 2
Multiply through by r cosΘ
r² (cosΘ - 1) = 2r cosΘ ==> r rcosΘ - r² = 2r cosΘ
Okay, so r cosΘ = x and r = √(x² + y²)
x √(x² + y²) - x² - y² = 2x
This is one form. If you really hate the radical, you can rearrange and square it.
x √(x² + y²) = 2x + x² + y²) ==> x² (x² + y²) = (2x + x² + y²)²
You can expand that and simplify it some.
4 x^3+x² y²+4 x²+4 x y²+y^4 = 0.
Multiply through by r cosΘ
r² (cosΘ - 1) = 2r cosΘ ==> r rcosΘ - r² = 2r cosΘ
Okay, so r cosΘ = x and r = √(x² + y²)
x √(x² + y²) - x² - y² = 2x
This is one form. If you really hate the radical, you can rearrange and square it.
x √(x² + y²) = 2x + x² + y²) ==> x² (x² + y²) = (2x + x² + y²)²
You can expand that and simplify it some.
4 x^3+x² y²+4 x²+4 x y²+y^4 = 0.