How do you find the eccentricity, directrix, focus and classify the conic section #r=10/(2-2sintheta)#?
1 Answer
See explanation and graph.
Explanation:
graph{sqrt(x^2+y^2)-5-y=0 [-10, 10, -5, 5]}
represents
( parabola ellipse hyperbola )
according as
Here, the form is
The eccentricity e = 1. So, the conis is a parabola.
The semi latus rectum 2a = 5. So, the size of the parabola a = 5/2.
The focus is at the pole r = 0.
The axis of the parabola makes an angle
The vertex V is in the opposite direction #theta =- pi/2, at a distance
a = 5/2. So, V is
The directrix is perpendicular to the axis at a distance 2a = 5 above
from the vertex. So, its equation is
by projection of the radius to
remembering that focus is at r = 0..