ircle; if it be on thecircumference, the locus is evidently the tangent at P. 43. To find the polar of any given point (^\y) withrespect to the circle x^+if = r-. Let QRS be the circle x^ + y-^r^, and P the givenpoint {x\ y). Let a chord through P cut the circle in 96 Analytical Geometry. Q{h, I)… … The tangents at (/^ A) and (7^, A-) arexli 4- ijli = r-,xh + yJi = /■-.Hence the co-ordinates of T satisfy these equations,and therefore the co-ordinates of T satisfyx{Ji-h) + y{l-Jc) = 0.But since {x\y) lies on the straight line through(/?, A-), {It, h), therefore (§ 15) x - h y - Jih - h A- -…
Geometry, Analytic
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