Please answer this a question , how to find an conic which passes 3 given points and has the given pole-polar pair. Does this determine the conic uniquely?
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The question is not very clear, so I have to make some assumptions. Let's give the names $A$, $B$, $C$ to the three points that the conic passes through (in that order).
When you say "has the given pole-polar pair", I'm assuming you mean that we are given some fourth point $D$ which is the pole corresponding to the line $AB$.
If my assumptions are correct, then this data does indeed determine the conic uniquely. In general, you need five point/tangent conditions to determine a conic. We have three points, obviously, and the fourth point $D$ gives you tangent lines $DA$ and $DC$.
When you say "find" the conic, what is it that you want to know about it? Or, saying it another way, in what form would you like to "know" it?
Whatever you want, this page probably has the answer.
If I remeber correctly I think that you must first find the correct coordinates where this comic point is located. Then find that the the thrid dimensional point on the grid as well.