Question

Which of the following points lies on the graph of r = 2 - 3cosθ?

Answer 1

The choices?

Answer 2

(-1, 0°)
(0, 0°)
(1, 0°)
(2, 0°)

Answer 3

for each of these points, the first coordinate is r and the second coordinate is θ

simply plug in the given r and θ values to see if the equation is true

Answer 4

for example, take the first point (-1, 0°) and let r = -1 and θ be 0 and see if r = 2 - 3cosθ is a true statement

Answer 5

Identify the conic whose equation is given.
r=2/3+5 sinθ
ellipse
parabola
hyperbola

Answer 6

Post in a new "Ask a question." so you're not warned or suspended..

Answer 7

@Zepdrix I don't remember how to do this may I have some assistance?

Answer 8

#1\[\large\rm r=\frac23+5\sin \theta\]

#2\[\large\rm r=\frac{2}{3+5\sin \theta}\]
Is it written like #1 or #2?
I just wanna make sure we start from the correct place.

Answer 9

written like#2

Answer 10

Let's start by multiplying through by our denominator,\[\large\rm r(3+5\sin \theta)\]

Recall that we have this relationship when going between Cartesian and Polar,\[\large\rm r^2=x^2+y^2\]\[\large\rm r=\sqrt{x^2+y^2}\]
\[\large\rm x=r \cos \theta\]\[\large\rm y=r \sin \theta\]

Answer 11

Woops I made a typo, step one should give us,\[\large\rm r(3+5\sin \theta)=2\]

Answer 12

Distributing,\[\large\rm 3r+5r \sin \theta=2\]

Answer 13

And then convert to Cartesian,\[\large\rm 3\sqrt{x^2+y^2}+5y=2\]

Answer 14

what would it be though? an ellipse, parabola, or a hyperbola.

Answer 15

And do some stuff,\[\large\rm 3\sqrt{x^2+y^2}=(2-5y)\]And square,\[\large\rm 3(x^2+y^2)=(2-5y)^2\]

You could go further, but from this point,
it looks like we're going to end up with both squared x's and squared y's with different coefficients.

So we have an ellipse.

There might be an easier way to identify the shape from the start :p
but I can't remember...

Answer 16

Err wait sorry lemme :)

Answer 17

I forgot about the subtraction XD I should be careful haha

Answer 18

I have another question. Write the equation of the conic satisfying the given conditions.

focus at the pole, e = 3/4, directrix rsinθ = -2

Answer 19

\[\large\rm 3x^2+3y^2 = 4-20y+25y^2\]
\[\large\rm 3x^2-22y^2+20y=4\]
Ya ya, we're subtracting the y's, completing the square with some value,\[\large\rm 3x^2-(y+c)^2=d\]So we end up with a hyperbola.

Ahh math is hard >.<

Answer 20

Hmm i dunno bout that next one :d

Answer 21

What is the argument of 3 - 3i?
300°
315°
330°
345°

Answer 22

The modulus of (1 + 2i)^4 is _____.
5
20
25
625

Answer 23

Which of the following is an argument of one of the fourth roots of 16(cos80° + isin80°)?