Identify (a) r=\frac{4}{1+3\sin \theta} (b) r=\frac{7}{1-3\cos \theta} (c) r=\frac{8}{6+5\cos \theta} (d) r=\frac{3}{2-3\sin \theta}

Bevan Mcdonald 2021-08-14 Answered

Identify each conic using eccentricity.
(a) r=41+3sinθ
(b) r=713cosθ
(c) r=86+5cosθ
(d) r=323sinθ
image

You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Ezra Herbert
Answered 2021-08-15 Author has 99 answers
Vasquez
Answered 2021-12-27 Author has 460 answers

Step 1

Let us find eccentricity of given function

We have to find eccentricity

if e=1, the conic is a parabola

if e=0, the conic is a circle

if e<1, the conic us an ellipse

if e>1, the conic is a hyperbola

r=ed1±esinθ

r=ed1±ecosθ

Step 2

Solution will be at end of step 2

a)r=41+3sinθ

r=41+3sinθ

e=3 (e>1, the conic is a hyperbola)

b) r=71cosθ

e=1(e=1, the conic is a parabola)

Step 3

c) r=86+5cosθ

r=86(1+56cosθ)

r=86(1+56cosθ)

r=43(1+56cosθ)

e=56

e=0.83, e<1 (the conic is an ellipse)

d) r=323sinθ

r=32(132sinθ)

r=322(132sinθ)

e=32

e=1.5 (e>1, the conic is a hyperbola)

Answer:

a) e=3

b) e=1

c) e=0.83

d) e=1.5

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more