How do you find the eccentricity, directrix, focus and classify the conic section r=102−2sin⁡θ?

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ljmolerovae · Accepted Answer

lr=1+ecos⁡(θ+α)  represents   (parabola ellipse hyperbola)   according as  (e=&amp;lt;&amp;gt;1)  Here, the form is  5r=1−sin⁡θ=1+cos⁡(θ+π2).  The eccentricity e=1. So, the conis is a parabola.   The semi latus rectum 2a=5. So, the size of the parabola a=52.   The focus is at the pole r=0.   The axis of the parabola makes an angle θ=α=π2.  The vertex V is in the opposite direction θ=−π2, at a distance  a=52. So, V is (52,−π2)  The directrix is perpendicular to the axis at a distance 2a=5 above from the vertex. So, its equation is  rsin⁡θ=−5.  by projection of the radius to (r,θ) upon the axis, remembering that focus is at r=0..

How do you find the eccentricity, directrix, focus and classify

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