Need help with conic intersection algebra

AI Thread Summary
To find the intersection points of the circle defined by x^2 + y^2 = 4 and the ellipse given by (x^2/4) + (y^2/9) = 1, the discussion focuses on algebraic manipulation of these equations. The user attempts to equate the two conics and simplifies to 5y^2 = 1, indicating a potential step towards finding y-values. Suggestions include plotting the graphs to visually identify intersections, although this may not assist in the algebraic solution required. Ultimately, the known intersection points are (-2,0) and (2,0), but the user seeks a detailed algebraic approach to arrive at these solutions. The conversation emphasizes the importance of step-by-step algebraic reasoning in solving conic intersections.
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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