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    • Thread Starter

    FP3/2 question here.
    It's pretty lengthy but might be a solid question (I'm not sure).

    The polar curve  r(1-\sin \theta )=4 is a parabola with Cartesian equation,
     \displaystyle y=\frac{1}{8} x^2 -2 .

    (a) Find the focus and directrix of the parabola.

    (b) A curve,  \text{C} , has equation  \sqrt{2(x^2+y^2)} + x=y+4\sqrt 2 .
    It is further given that the curve  \text{C} is a conic section.
    Find in any order the following of  \text{C}

    (i) The type of conic section.
    (ii) The eccentricity.
    (iii) The focus/foci and directix/directrices.
    (iv) The line of symmetry.
    (v) The polar equation.

    What have you tried so far?
    • Thread Starter

    (Original post by Zacken)
    What have you tried so far?
    I always wondered what the equation of a rotated parabola would look like. So when I remembered, I thought I'd investigate and came up with what I think is quite an intriguing question. I would never guess the equation for C was a parabola by just looking at it. Quite beautiful.
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Updated: May 3, 2016

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