Help with conic intersections using algebra

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The discussion focuses on finding intersection points between lines and conic sections (ellipses and hyperbolas) using algebraic methods. Participants express uncertainty about completing their solutions after determining parameters like b and a² for the conics. A key point raised is the ambiguity in defining the specific conic sections, as multiple ellipses and hyperbolas can pass through the given points. The need for additional information about the conics is emphasized to proceed with the calculations. Overall, the conversation highlights the challenges of solving intersection problems without complete definitions of the conic shapes involved.
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Homework Statement


Find the intersection points of: Line through (3,1) with slope -1/2, and ellipse through (-3,0) and (-2,2). No graphing just algebra.


The Attempt at a Solution


So far I have b=10/4 and a^2=9. I'm not sure how to finish this problem.

Homework Statement


Find the intersection point of: Line through (-1,-1) with slope 2, and hyperbola through (2,0) and (-3,-1). No graphs just algebra.



The Attempt at a Solution


So far I have b=1 and a^2=4. Again, not sure where to go from here. Any pointers?
 
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Cacophony said:

Homework Statement


Find the intersection points of: Line through (3,1) with slope -1/2, and ellipse through (-3,0) and (-2,2). No graphing just algebra.


The Attempt at a Solution


So far I have b=10/4 and a^2=9. I'm not sure how to finish this problem.

Homework Statement


Find the intersection point of: Line through (-1,-1) with slope 2, and hyperbola through (2,0) and (-3,-1). No graphs just algebra.



The Attempt at a Solution


So far I have b=1 and a^2=4. Again, not sure where to go from here. Any pointers?

There are zillions of ellipses passing through (-3,0) and (-2,2). What haven't you told us? Same with the hyperbola.
 

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