Proof of normal to hyperbola (1 Viewer)

[edd91]

Can someone write out the complete proof for me, i cant get to the 'standard' equation

 

[kimmeh]

which one ? parametrics or normal xy?
your textbook should prove it for you anyway.

 

[Teoh]

Just differentiate the equation of the normal hyperbola to find gradient of tangent
Reciprocate that, and use two point formula with cartesian or paramteric co-ordinates to give you equation.

 

[Heinz]

Originally posted by Teoh
Just differentiate the equation of the normal hyperbola to find gradient of tangent
Reciprocate that, and use two point formula with cartesian or paramteric co-ordinates to give you equation.

You mean minus the reciprocal of the gradient

 

[Teoh]

Originally posted by Heinz
You mean minus the reciprocal of the gradient

I can neither confirm, nor deny that comment...:mad1:

 

[Affinity]

you can acquiesce

 

[edd91]

parametric form
I know the process to get to it but I just cant??I get to this:

-xy1/a^2 + yx1/b^2= -yx/b^2 - xy/a^2

then dont know how to get to my target

 

[grimreaper]

Originally posted by edd91
parametric form
I know the process to get to it but I just cant??I get to this:

-xy1/a^2 + yx1/b^2= -yx/b^2 - xy/a^2

then dont know how to get to my target

Erm well you've done something wrong because thats wrong... try doing it again. You should end up with an x1^2/a^2 and a y1^2/b^2, which when you subtract the second from the first = 1

 

[kimmeh]

Originally posted by Affinity
you can acquiesce

english would be nice