How do you find the eccentricity, directrix, focus and classify the conic section #r=0.8/(1-0.8sintheta)#?
1 Answer
Please see below.
Explanation:
It is a typical equation of an ellipse in polar form. However, it is easier to identify conic section, its eccentricity, directrix and focus in rectangular coordinates. Hence, let us convert the polar equation in rectangular form.
The relation between polar form
Hence
or
or
or
or
or
or
or
Hence, this is the equation of an ellipse of the form
whose center is
eccentricity is given by
=
Focii are
and directrix are
i.e.
graph{(25x^2+9y^2-32y-16)(x^2+y^2-0.01)(x^2+(y-32/9)^2-0.01)(y+1)(y-41/9)=0 [-6.31, 6.346, -1.44, 4.884]}