Find the polar equation of the conic with the focus at the pole, directrix y = -6, and eccentricity 4

Mathematics

1 answer:

expeople1 [14]3 years ago

3 0

Answer:

Choice B is correct

Step-by-step explanation:

The eccentricity of the conic section is given as 4 and thus the conic section is a hyperbola. Hyperbolas are the only conic sections with an eccentricity greater than 1.

Next, the directrix of this hyperbola is located at y = -6 implying that the hyperbola will be opening upwards. Consequently, the polar equation of this hyperbola will be of the form;

$r=\frac{k}{1-4sin(theta)}$

The value of k in the numerator is the product of eccentricity and the absolute value of the directrix;

k= 4*6 = 24

The polar equation is thus given by alternative B

You might be interested in

Will mark brainliest to whoever answer’s tgese question’s

Blababa [14]

I don’t get it?? Sorry

7 0

3 years ago

What is the correct name for the angle shown

Vesna [10]

Answer:

i dont see no angle

Step-by-step explanation:

4 0

3 years ago

Un número que multiplicado te de 12 y restado de 7.

maksim [4K]

Answer84

Step-by-step explanation:

4 0

2 years ago

A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder increases and the radius, r, decr

Elena L [17]

Answer:

$0.0727 cm\: per\: second$

Step-by-step explanation:

The Volume of the cylinder is constant

Volume of a cylinder, $V=\pi r^2h$

Given:

$\frac{dh}{dt}=0.8 cm/sec\\ r=2cm\\h=11cm\\\frac{dr}{dt}=?$

$\frac{dV}{dt}=\pi r^2 \frac{dh}{dt} + 2\pi r h\frac{dr}{dt}$

$0=\pi* 2^2*0.8 + 2\pi*2*11\frac{dr}{dt}\\0=3.2\pi+44\pi\frac{dr}{dt}\\44\pi\frac{dr}{dt}=-3.2\pi\\\frac{dr}{dt}=\frac{-3.2\pi}{44\pi} \\\frac{dr}{dt}=-0.0727 cm\: per\: second$