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

Question

Graph the conic and find the values of e, a, b, and c:
r=14/3+4cos(theta)

Answer 1

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(e² - 1) / (1 + e cosθ)

 

with eccentricity

 

e = 4/3 > 1.

 

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

 

a(e² - 1) = 14/3

 

a[(4/3)² - 1] = 14/3

 

Solve 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.