conics question.. from cambridge (1 Viewer)

[conkerbuyore744]

can anyone help me with this conics question

P and Q are variable points on the rectangular hyperbola xy=9
the tangents at P and Q meet at R.
if PQ passes through the point (6,2) find the equation of the locus of R



the answer is x+3y=9


Thanks!!!

 

[pLuvia]

ALl you do is find the coordinates of R, so find the tangents at P and Q then solve them simultaneously to find R.
Then you will have an x and y coordinate for R
eg x=?
y=?

Join both of those equations together so that you have no other variables other than x and y then the locus of R is that equation

 

[haque]

Try it urself before u look at the solution but here it is anyway
P93p,3/p) and the same for Q except the parameter is q when we find the equation of the tangetns at P and Q we get R as the intersection point with R(6pq/p+q, 6/p+q) also the equation of PQ chord is x+pqy=3(p+q) and the point 6,2 satisifes so sub this in and u get 2pq=3(p+q)-6 and sub this back for the x coordinate of R and u get x=9(p+q)/p+q -18/p+q=9-3y and u get the result.