GEOMETRY 



45 



2.400 Parabola (Fig. 3). 



2.401 O, Vertex; F, Focus; 

 ordinate through D, Direc- 

 trix. 



Equation of parabola, 

 origin at O, 



x = OM, y = MP, 

 OF = OD = a 

 FL = 20, = semi latus 



rectum. 



FP = D'P. 



2.402 FP = FT 



= x + a. 



FIG. 3 



NP = 2Va(a + x), TM = 2X, MN = 20, ON = x + 20. 



, OS = ( + 2a) ( 



ON' = \ (x + 2 a), OQ = 



F.S perpendicular to tangent TP. 

 F5 = Va(a + x), TP = 2r5 = 2V x (a + *). 



T5 2 = Fr XFO = FPX FO. 



The tangents 2T and t/"P' at the extremities of a focal chord PFP' meet 

 on the directrix at U at right angles. 



T = angle 



tan r = y - 



The tangent at P bisects the angles FPD' and 

 2.403 Radius of curvature: 



Coordinates of center of curvature: 



Equation of Evolute: 



2 'jay 2 = ^(x 20)*. 



