174 
ELLIPSE. 
5. About the centre of an ellipse 
is described a circle, with a radius equal to the ordinate: to find 
the locus of the intersection of this circle with the ordinate. 
The required locus is an ellipse defined by the. equation 
Lardner: Algebraic Geometry, p. 151. 
Section II. 
Referred to its Axes. Tangents. 
1. If (a, /3), (a, /3'), be the coordinates of two points in a 
diameter of an ellipse, and be subject to the condition 
to find the equations to the tangents at the extremities of this 
diameter. 
If x, y, be the point of contact, 
But, the points (a, /3), and (a', /S'), lying in the same line 
with the point (x, y), 
x a. a! 
and therefore 
hence, from (1), 
and consequently, by the condition of the problem, 
X — ± (ckx'Ÿ • 
y = ± mt 
similarly