Explain why it is not possible for a hyperbola to have foci at (0...

Question

Explain why it is not possible for a hyperbola to have foci at (0,-2) and (0,2) and vertices at (0,-3) and (0,3).

Accepted Answer

Hello today we're going to give a reason as to why it's not possible to have a faucet and Verdecia hyperbole to when our foes i is plus or minus one comma zero and our vertex is our plus and minus two comma zero. So just to quickly state one thing in most textbooks, Fosse is normally labeled as plus or minus C comma zero and our vertex is Are normally labeled as plus or -10. So let's just quickly recall what the general graph of a hyperbole is. So a hyperbole always has a set of ASM totes where typically one set of asientos looks like a box and the other intersect the corners of that box and we have the vertex is of the parabola just slightly close to the limit of this box where the parabola opens up on both sides. So again this is going to be a and our fosse are slightly to the right and left of our vertex is so our fosse are gonna be located right in front of our vertex is of the parabola. So C is going to be here and here. So just looking at this graph or at least pay attention to the right hand side of this graph, C. Is always going to be greater than a. And with our given fosse are positive values for our fosse is going to be one and our positive value for the vertex is is going to be too. So if we were to put this on a hyperbole to what this is saying is we have our vertex is for the parabolas at two. But our focus I are located behind the vertex, which is not correct. So the reason why it's not possible to have our fosse of plus or minus one comma zero and our verses of plus or minus two comma zero on the same hyperbole is because our focus I must be always greater than our versus is. So that means that for hyperbole as C must always be greater than a. And the answer to this problem is going to be be So I hope this video helps you in understanding why you need to have a certain value for fosse and vergis is for hyperbole as and I'll go ahead and see you all in the next video.

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