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Find the polar equation of the conic with the focus at the pole, directrix x = -5, and eccentricity 2.

Find The Polar Equation Of The Conic With The Focus At The Pole Directrix X 5 And Eccentricity 2 class=

Sagot :

Step-by-step explanation:

Given that,

Directrix, d= -5, and eccentricity, e = 2.

The polar equation of the conic is given by :

[tex]r=\dfrac{ed}{1-e\cos\theta}[/tex]

Put all the values,

[tex]r=\dfrac{-5\times 2}{1-2\cos\theta}\\\\=\dfrac{-10}{1-2\cos\theta}[/tex]

As e>1, it is a hyperbola. Hence, this is the required solution.

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