nit- i iM' 



The m is accomplished most easily by squaring each 



member of equations (4) and <:.). and adding: 



thisgives (1 



Henoe, t> ,.,.- the circle 



is, Ike locut u/ Ike foot of a perpendicular from titMer focus upon a Inn- 

 'he etlipte it ike major auxiliary cii 



151. The locus of the intersection of two perpendicular tangents to the 

 ellipe*. 



Let the equation of any tangent to the ellipse ^ + J* = 1 be v 



the for m (Art. It 



y - mx = Vam* + A*, . . (1) 



then the equation of a perpendicular tangent U 



f+a-** 



U, my 4 x = Va + Wsi. 



P' = (r',y') te the jniint of int**r*rtion of these two Ungents, 

 (1) a is required to tin.l ti..- IOCUM of f as M varies in value; 



I, t< tin.l an .- put ion between r 1 and y* which does not involve M. 

 Proceeding as in Art. i:.o : .nino- /' i> on both liue.n (1) and ( 



th.-r.-f.-r.- y' - m** 



To eliminate n, aquare both equations, and add : thia gives 



Therefore, the point of intersection of perpendicular tangent* is on 

 the circle 



r + y = + 6. [fll] 



which is called the director circle for the ellipee. Tie tocut of tke inirr 

 tcfion of too p*rp*uKcular tangent* to an ellipte u, lken t in Erector ctrrlf. 



