I'm having trouble with this problem. Any help would be appreciated.
The normal at any point on the hyperbola x^2/a^2 - y^2/b^2 = 1 intersects the x and y axes at P and Q respectively. Find the locus of the midpoint of PQ.
Thanks
The hyperbola can be defined by the following parametric equations:
.
Then .
The equation of the tangent can be written using the model : .
Use this equation to get the coordinates of the x- and y-intercepts, that is, the coordinates of P and Q. Use these coordinates to get the midpoint of PQ.
You now have the parametric equations of the required locus. Convert them into a Cartesian equation if required.
Warning: My carelessness is a well documented fact. The above results may contain errors. You should work through the calculations very carefully for yourself.