sketch the conic r=2/1+cos theta
4 answers
since e=1, it is a parabola, with vertex at (0,1) opening to the left.
Perhaps you feel more comfortable with rectangular graphing
r=2/1+cos theta
r = 2/(1+ x/r)
r + x = 2
√(x^2 + y^2) + x = 2
√(x^2 + y^2) = 2-x
square both sides
x^2 + y^2 = 4 - 4x + x^2
y^2 = 4 - 4x
Steve meant to say, vertex is (1,0)
r=2/1+cos theta
r = 2/(1+ x/r)
r + x = 2
√(x^2 + y^2) + x = 2
√(x^2 + y^2) = 2-x
square both sides
x^2 + y^2 = 4 - 4x + x^2
y^2 = 4 - 4x
Steve meant to say, vertex is (1,0)
in (r,θ) it is (0,1)
in (x,y) it is (1,0)
in (x,y) it is (1,0)
Dang - did I really say that?
(1,0) in either case!
(1,0) in either case!