Finding intersection points of circle x² + y² = 4 and ellipse x²/4 + y²/9 = 1

[Cacophony]

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?

 

[Dick]

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?

 

[Cacophony]

Oh ok, so the answer is 5y^2=1?

 

[Dick]

Oh ok, so the answer is 5y^2=1?

Why would you get that? Reread my last post.

 

[jkristia]

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

 

[kushan]

hey cacophony , just plot the two graphs and you will see the intersection

 

[Mark44]

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.