Elements of analytical geometry and the differential and integral calculus . X from the origin, for the center of the circle ; —to the right, if c is negative, and to the left, if c is positive. Then from the center, with a radius equal to R=j2p-\-c^fdescribe a circle cutting the line drawn midway between the twoaxes, as in the fignire. In this example the center of the circle is at C, the distance oftwo units from the origin A, to the right. Then, with the we described the circle, cutting the line in M and M\ andwe find by measure (when the construction is accurate) thatjl/P=,
Elements of analytical geometry and the differential and integral calculus . X from the origin, for the center of the circle ; —to the right, if c is negative, and to the left, if c is positive. Then from the center, with a radius equal to R=j2p-\-c^fdescribe a circle cutting the line drawn midway between the twoaxes, as in the fignire. In this example the center of the circle is at C, the distance oftwo units from the origin A, to the right. Then, with the we described the circle, cutting the line in M and M\ andwe find by measure (when the construction is accurate) thatjl/P=, the positive root, and MP=^—, the negativeroot. For another example we require the roots of the follovjing equa-tion hy construction: y2+6y=27. N. B. When the numerals are too large in any equation forconvenience, we can always reduce them in the following manner:Put y=nz, then the equation becomes ^i5 22_|_g^2=27. n, 2 I 6 27 Or z^-\--z — n n Now let w= any number what-ever. If n=S, thenz^-\2z=3, Herec=2. tl ^=3. 2 Whence E=JlO=3A6, At the distance of two units. CONIC SECTIONS. 41 to tlie left of the origin, is the center of the circle. We see bythe figure that 1 is the positive root, and —3 the negative root. But y=w5?, n=3, 2=1, y=3 or —9. We give one more example. Construct the equation Here c=4, and -^^=—6. Whence i2= Using the same figure as before, the center of the circle tothis example is at D, and as the radius is only 2, the circum-ference does not cut the line MM, showing that the equationhas no real roots. We have said that this method of finding the roots of a quad-ratic vras of little practical value. The reason of this conclu*sion is based on the fact that it requires more labor to obtainthe value of the radius of the circle than it does to find theroots themselves. Nevertheless this method is interesting and instructive as analgebraic geometrical problem. When we find the polar equation of the parabola, we shall thenhave another method of con
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