An Introduction to the Infinitesimal Calculus Notes for the Use of Science And

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(l-e2) (l-e2)2', 2 y2 Putting a2 = and ^>2 = (1 - e2)2 (1 _ e2) ri2e2 (1 - ^2)2 d^ 1 - «2' /Tr'2 . 1*2 we have l + f^'^-^' where ^2 = 0^2^1 _g2^. In this form the origin C is called the centre of the curve, since it bisects every chord which passes through it. This is a;2 y2 clear, since if {x^, y^) lies on -2 + T2= 1> so does {-x^, -Vi)- d de^ Also we notice that CS = . ; 5 -d=, — —. = ae, and that CX=--^ = -. I - e2 g From the symmetry of the equation a;2 y2 a2 + 62-J' it is clear that there ...is another focus, namely, the point {ae, 0) ; and another directrix, the line aj = -, with regard to the axes through the point C. 86 THE CONIC SECTIONS The axis of x is in this case called the major axis, and the axis of y the minor axis. The one is of length 2a ; the other of length 2h. If h had been greater than a, the foci would have lain upon the axis of y, and this axis would have been the major axis. When a and h are known, the eccentricity e is given by In the circle a—h^ and e = 0.

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