a) Find M first. M [(p+q)/2 , (1/p+1/q)/2)
Skipped some steps, used gradient formula to find gradient of PQ.
Gradient of PQ= -1/(pq)
Skipped some steps, used gradient formula to find gradient of OM.
Gradient of OM= 1/pq
Given: Gradient of OM x Gradient of PQ = -1
(Therefore) -1/(pq)^2 = -1
(Therefore) q = 1/p
b) Using the formula for tangent of a hyyperbola, (x.x1/a^2 - y.y1/b^2=1)
eqn of tgt at P: px/a^2- y/pb^2 =1
eqn of tgt at Q: x/pa^2 - yp/b^2 =1 (q=1/p, from above)
(To be Continued, let me finish it on paper)
