Need help with conic intersection algebra

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Homework Help Overview

The discussion revolves around finding the intersection points of a circle and an ellipse, both centered at the origin. The specific equations given are for a circle defined by x² + y² = 4 and an ellipse defined by (x²/4) + (y²/9) = 1.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to manipulate the equations to find a solution but expresses uncertainty about the steps needed to reach the known intersection points. Participants question the reasoning behind certain algebraic manipulations and suggest examining the geometric properties of the figures involved.

Discussion Status

The discussion is ongoing, with participants providing various insights and suggestions. Some guidance has been offered regarding algebraic manipulation and graphical representation, but there is no explicit consensus on a method or solution yet.

Contextual Notes

Participants note the importance of understanding the relationship between the shapes involved, such as the vertices of the ellipse and the radius of the circle, while also recognizing that plotting the graphs may not directly aid in identifying the intersection points as required by the problem.

Cacophony
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Homework Statement



Find intersection points of the following.(Conics are centered to origin)

Circle = x^2+y^2=4, Ellipse = (x^2/4)+(y^2/9) = 1


The Attempt at a Solution



So far I have this. (BTW I know the solutions are (-2,0) and (2,0) but I'm still unsure how to get there step by step).

(x^2/4)+(y^2/4) = (x^2/4)+(y^2/9)= 1

What's the next step?
 
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If you have (x^2/4)+(y^2/4) = (x^2/4)+(y^2/9) what do you get if you subtract (x^2/4) from each side?
 
Oh ok, so the answer is 5y^2=1?
 
Cacophony said:
Oh ok, so the answer is 5y^2=1?

Why would you get that? Reread my last post.
 
I'm not sure exactly how to solve this, but I would look at the vertices of the ellipse and the radius of the circle
 
hey cacophony , just plot the two graphs and you will see the intersection
 
kushan said:
hey cacophony , just plot the two graphs and you will see the intersection
But that will probably not help the OP in identifying the intersection points, which is what the problem asks him/her to do.
 

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