CIRCLE. 
Section I. 
Referred to two Perpendicular Diameters. Tangents. 
1. To find the relation among the quantities a, Z>, c, that 
the line x y 
- + t = 1 
a b 
may be a tangent to the circle 
x 2 + f = c 2 . 
If a be the inclination of the radius of any point in the 
circumference to the axis of ce, the equation to the corresponding 
tangent is x cos a + y sin a = c. 
In order that this equation may coincide with that to the 
given straight line, we must have 
cos a 
sin a 
Squaring and then adding these equations, we get, for the 
required relation, 111 
9 O "f" Vo ■ 
2. Tangents are drawn to a circle 
x* + if = d 
at two points (af, y), (x\ y"): to find the distance of a point 
(h, k) from a line passing through the centre of the circle and 
the intersection of the two tangents. 
The equations to the two tangents are