# Math Help - Two Conic equations!

1. ## Two Conic equations!

Well the teacher didn't get to this section and teaching myself did not work well lol.. I partly understand to an extent.

The first example goes like
Sketch the graph of the equation r = 3/(2-2sinθ)

Now I doubt you'd be able to graph on this website, but I am wondering how to get to it.

I know that, R= 3/(2-2sinθ) then R=3/2(1-sinθ) therefore R= (3/2) / 1-sinθ
and since a=1, it is a parabola

the next step goes like θ R but how do you work that into a graph?

Second, would be ... Find an equation for the conic section r=1/(1+3sinθ) and i am less confident what to do on this part...

2. Originally Posted by aargh27
Well the teacher didn't get to this section and teaching myself did not work well lol.. I partly understand to an extent.

The first example goes like
Sketch the graph of the equation r = 3/(2-2sinθ)
r=3/(2-2sin θ)

2r-2rsin θ=3
2r-2y=3
2r=3+2y
(2r)^2=(3+2y)^2=9+12y+4y^2
Thus,
4x^2+4y^2=9+12y+4y^2
4x^2-9=12y

Is the conic (it is a parabola).

3. I just worked out second problem.
Is this right?

r+3rsinθ=1
r+3y=1
r^2 +3y^2=1
X^2 + y^2 +3y^2=1
x^2 + 4y^2 =1

4. Originally Posted by aargh27
I just worked out second problem.
Is this right?

r+3rsinθ=1
r+3y=1
r^2 +3y^2=1
The mistake is here, not (a+b)^2 not = a^2+b^2
(You need to multiply all possible products of the terms).

r+3y=1
r=1-3y
r^2=(1-3y)^2
x^2+y^2=1+6y+9y^2
Now, combine and simplify.

5. Hello, aargh27!

Sketch the graph of the equation: .r .= .3/(2 - 2·sinθ)

I know that: .r .= .3/(2 - 2·sinθ) .= .r .= .1.5/(1 - sinθ)
and since a=1, it is a parabola. . Right!

the next step goes like: .θ .R
but how do you work that into a graph?

We already know that it's a parabola.
. . And it opens in one of four directions: left, right, up, or down.

Plot points in the four compass-directions to get its orientation.

θ = 0: . r .= .1.5/(1 - 0) .= .1.5

θ = π/2: . r .= .1.5/(1 - 1) undefined . . . The parabola opens upward.

θ = π: . r .= .1.5/(1 - 0) .= .1.5

θ = 3π/2: . r .= .1.5/(1 - [-1]) .= .0.75

This is enough to sketch the parabola.
Code:
                      |
*            |            *
|
*           |           *
|
- - - o - - - - + - - - - o - - -
1.5        |        1.5
*     |     *
*o*
|0.75
|