How do you find the eccentricity, directrix, focus and classify the conic section #r=14.4/(2-4.8costheta)#?

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Answer 1 · 2016-09-19T12:49:15

See below.

We have

#r = a/(b-c costheta)# or

#sqrt(x^2+y^2) = a/(b - c x/sqrt(x^2+y^2))# or

#sqrt(x^2+y^2)=(asqrt(x^2+y^2))/(bsqrt(x^2+y^2)-cx)# or

#1=a/(bsqrt(x^2+y^2)-cx)# or
#bsqrt(x^2+y^2)-cx = a# or

#x^2+y^2 = (cx+a)^2/b^2# or

#(1-c^2/b^2)x^2+y^2-(2ac)/b^2x=a^2/b^2#

so we have supposing #b ne 0#

#c=b# parabola
#c > b# hyperbola
#c < b# ellipse
#c = 0# circle