Help with conic intersections

[Bad@math]

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.

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

So far i've found b and a^2 for both equations but I do not know where to go from there.

 

[tkhunny]

Are you sure those are sufficiently well-defined? Do those two points constitute a unique conic section? Perhaps there is more information that you are not sharing?

 

[soroban]

Hello, Bad@math!

1. Find the intersection points of:
. . the line through (3,1) with slope -1/2, and the ellipse through (-3,0) and (-2,2).

So far i've found b and a^2. . What?
but I do not know where to go from there.

There are zillions of ellipses that contain those two points.

Here is one of them:

            |
            * * *
          * |     *
        o   |       *
       *    |        *
            |
  - - o - - + - - - - * - -
      *     |         *
      *     |         *
            |
       *    |        *
        *   |       *
          * |     *
            * * *
            |

Which ellipse are we supposed to use?