# 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]}