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Hyperbola and parabola

AS level maths (possibly further maths)

How do I find tangents (or parts of a tangent like m or c, when given one of the two) to ellipses, parabola and hyperbola.

I also need help on transformations of these things, including vector transformations.

I never did this in class so any help or notes or resources is really appreciated!!! Thanks
Original post by bee-m510
AS level maths (possibly further maths)

How do I find tangents (or parts of a tangent like m or c, when given one of the two) to ellipses, parabola and hyperbola.

I also need help on transformations of these things, including vector transformations.

I never did this in class so any help or notes or resources is really appreciated!!! Thanks


For all of them, just substitute your incomplete tangent eq. into your parabola/hyperbola/ellipse.

You will always end up with a unique answer if you're dealing with a parabola/hyperbola, but there will always be 2 possible tangents for an ellipse.

Anyway, just look at your module book for these things and make notes on it.
Original post by RDKGames

You will always end up with a unique answer if you're dealing with a parabola/hyperbola, but there will always be 2 possible tangents for an ellipse.


I'm sure you meant to say for a given gradient, unique for a parabola and 2 possible for ellipse or hyperbola.
Original post by bee-m510
AS level maths (possibly further maths)

How do I find tangents (or parts of a tangent like m or c, when given one of the two) to ellipses, parabola and hyperbola.

I also need help on transformations of these things, including vector transformations.

I never did this in class so any help or notes or resources is really appreciated!!! Thanks


Look here in the relevant module if you are old spec: http://www.drfrostmaths.com/resources/sow.php?year=A%20Level&term=C3
Original post by ghostwalker
I'm sure you meant to say for a given gradient, unique for a parabola and 2 possible for ellipse or hyperbola.


Ah dear... Yeah thanks, I overlooked the hyperbola situation in my head.
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Original post by RDKGames
For all of them, just substitute your incomplete tangent eq. into your parabola/hyperbola/ellipse.

You will always end up with a unique answer if you're dealing with a parabola/hyperbola, but there will always be 2 possible tangents for an ellipse.

Anyway, just look at your module book for these things and make notes on it.


I’ve tried doing this and just end up with a quadratic involving m or c that I can’t solve? And not sure what you mean by module book as we haven’t been given any books and i can’t find anything online on this topic

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