Conic Sections: Graphing with Multiple Squares

In summary: Yes, I think you're right. a should be greater than b in that case. If a = b, then the equation would become sqrt(a^2 - b^2) and the answer would be the same.In summary, the student is attempting to find c, which is the square root of a^2 - b^2. However, they are stuck because they are missing information about a and b.
  • #1
duki
264
0

Homework Statement



graph the following

Homework Equations



[tex]9x^2+4y^2+36x-8y+4=0[/tex]

The Attempt at a Solution



I think I need to get it into [tex]\frac{(x-x0)^2}{a^2}+\frac{(y-y0)^2}{b^2}[/tex] but I'm not sure.
I have [tex]\frac{9x^2}{-4}-8x+y^2-2y=1[/tex] and now I'm stuck
 
Last edited:
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  • #2
Ok, update. Here's what I have so far:

[tex]\frac{(x+2)^2}{2^2}+\frac{(y-1)^2}{3^2} = 1 [/tex]

Does that look right?
 
  • #3
It looks fine, if you meant 4y^2 in the original post and not 47^2.
 
  • #4
Thanks for catching that. I fixed it.
Ok, so now I have the following:

[tex]Center = (-2,1)[/tex]
[tex]a = 2[/tex]
[tex]b = 3[/tex]
[tex]Verticies: (0,1),(-4,1),(-2,4),(-2,-2)[/tex]

Does that look right?
 
  • #5
Looks right to me. But I'm tired. You should double check.
 
  • #6
haha. you're supposed to be the double checker!

I'm really stuck now. I'm trying to find 'c' and I get [tex]\sqrt{-5}[/tex]. Did I do something wrong? c is the square root of a^2 - b^2 right? Here, a = 2 and b = 3. I'm confused
 
  • #7
No. YOU are supposed to be the double checker. It's your class. I'm just tossing off hints without being fully awake. I have no idea what 'c' is supposed to be. Could you just like say what it is supposed to be instead of dropping a cryptic letter? I'll take another guess and say 'distance from center to focus'? That's a lot better description than 'c'. Why don't you think it could be sqrt(3^2-2^2)? If you flip the x and y axes, do you think this distance should change from real to imaginary?
 
  • #8
hmm, I'm not sure. I didn't know you could swap them like that. The formula I was going by said "distance from center to focus" = sqrt(a^2 - b^2). If you flip them, you get the real answer?
 
  • #9
Surely that formula was assuming a> b. That is, that a is the length of the longer semi-axis. Don't just memorize formulas. Learn what the mean.
 

Related to Conic Sections: Graphing with Multiple Squares

1. What are conics with multiple squares?

Conics with multiple squares are geometric figures that are created by intersecting multiple squares. They are also known as square conics or conic sections.

2. What are the different types of conics with multiple squares?

There are three main types of conics with multiple squares: the ellipse, the hyperbola, and the parabola. These are determined by the angle at which the intersecting squares are placed and the relative size of the squares.

3. How are conics with multiple squares used in real life?

Conics with multiple squares have many practical applications in fields such as engineering, architecture, and astronomy. They are used to create curved structures, such as bridges and domes, and to model the orbits of celestial bodies.

4. What is the focus of a conic with multiple squares?

The focus of a conic with multiple squares is the point within the figure that determines its shape. For an ellipse, the sum of the distances from any point on the ellipse to the two foci is constant. For a parabola, the focus is the point of intersection between the parabola and its axis of symmetry. For a hyperbola, there are two foci, and the difference of the distances from any point on the hyperbola to the two foci is constant.

5. How do you graph a conic with multiple squares?

To graph a conic with multiple squares, you will need to know the coordinates of the focus and the equation of the conic. This information can then be used to plot the points and draw the curve. Alternatively, you can use a graphing calculator or computer software to graph the conic for you.

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