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Pegov1

Answered question

2022-02-12

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

r = \frac{14.4}{2 - 4.8 \cos θ}

Anahi Pearson

Beginner2022-02-13Added 16 answers

We have

r = \frac{a}{b - c \cos θ}

\sqrt{x^{2} + y^{2}} = \frac{a}{b - c \frac{x}{\sqrt{x^{2} + y^{2}}}}

\sqrt{x^{2} + y^{2}} = \frac{a \sqrt{x^{2} + y^{2}}}{b \sqrt{x^{2} + y^{2}} - c x}

1 = \frac{a}{b \sqrt{x^{2} + y^{2}} - c x}

b \sqrt{x^{2} + y^{2}} - c x = a

x^{2} + y^{2} = \frac{{(c x + a)}^{2}}{b^{2}}

(1 - \frac{c^{2}}{b^{2}}) x^{2} + y^{2} - \frac{2 a c}{b^{2}} x = \frac{a^{2}}{b^{2}}

so we have supposing

b \neq 0

c = b

parabola

c > b

huperbola

c < b

ellipse

c = 0

circle

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