rect hyperbola (1 Viewer)

[ibrian]

P(ct, c/t) lies on rectangular hyperbola xy=c^2. the normal at P meets the hyperbol again at Q. M is midpoint of PQ. find the equation of the locus of M

 

[kaz1]

Differentiate xy=c²
Find gradient of normal
Find equation of normal
Simultaneously solve equation of normal with hyperbola
Find Q
Find midpoint of PQ
Eliminate t

Sorry but that that's too much algebra for me to type up.

 

[ibrian]

yea im just having trouble finding Q

 

[Affinity]

You don't need to solve for Q in this question.

 

[undalay]

From the equation of the normal. If you sub it in to the rect hyperbola you will get a quadratic the roots which are P and Q (either in x or y)

To find midpoint, you can just do (sum of roots / 2). where sum of roots = -b/a

Then sub ur midpoint (either in x or y) in the normal, to find ur other coordinate.

 

[Drongoski]

That's a good approach.

 

[GUSSSSSSSSSSSSS]

From the equation of the normal. If you sub it in to the rect hyperbola you will get a quadratic the roots which are P and Q (either in x or y)

To find midpoint, you can just do (sum of roots / 2). where sum of roots = -b/a

Then sub ur midpoint (either in x or y) in the normal, to find ur other coordinate.

xD this is something i keep forgetting from time to time

.....good thing i remembered it during the half yearly exam xD