Help with conic intersections using algebra

[Cacophony]

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?

 

[LCKurtz]

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.