Zachary B.

asked • 09/30/17# Graph the conic and find the values of e, a, b, and c:

Graph the conic and find the values of e, a, b, and c:

r=14/3+4cos(theta)

r=14/3+4cos(theta)

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## 1 Expert Answer

Arturo O. answered • 09/30/17

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I will assume you meant

r = 14 / (3 + 4cosθ)

Divide numerator and denominator by 3 and get

r = (14/3) / [1 + (4/3)cosθ]

Note this is an equation of the form

r(θ) = a(e

^{2}- 1) / (1 + e cosθ)with eccentricity

e = 4/3 > 1.

This is the equation of a hyperbola since e > 1.

a(e

^{2}- 1) = 14/3a[(4/3)

^{2}- 1] = 14/3Solve this equation for a. One you have a, get c from

c = ea

Look up in your textbook the relation between b and these other quantities for a hyperbola, and solve for b. You should be able to finish from here.

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Arturo O.

09/30/17