This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1904 Excerpt: ...equal. 12. Any point on an equilateral hyperbola is the middle point of that part of the normal included between the axes of the hyperbola. 13. A circle is drawn through a point on the minor axis of an ellipse and through the foci. Show that the lines drawn through the given point and the points of intersection of the ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1904 Excerpt: ...equal. 12. Any point on an equilateral hyperbola is the middle point of that part of the normal included between the axes of the hyperbola. 13. A circle is drawn through a point on the minor axis of an ellipse and through the foci. Show that the lines drawn through the given point and the points of intersection of the circle and ellipse are normal to the ellipse. 14. How many normals may be drawn through a given point to (a) an ellipse? (b) an hyperbola? (c) a parabola? CHAPTER X RELATIONS BETWEEN A LINE AND A CONIC. APPLICATIONS OF THE THEORY OF QUADRATICS 90. Relative positions of a line and conic. If a Hue and conic are given, it is evident that (a) the line is a secant of the conic, (b) the line is tangent to the conic, or (c) the line does not meet the conic. The coordinates of the points of intersection of the line and conic are found by solving their equations (Rule, p. 76), which are of the first and second degrees respectively. To solve, we eliminate y and arrange the resulting equation in the form (1) Ax + Bx + C = 0. Denote the roots by xx and x., and the discriminant B2-4 A C by A. Analytically the three cases above present themselves as follows: (a) If A is posit ire, the fine is a secant. For Xi and x- are real and unequal (Theorem II, p. 3), and hence they are the abscissas of the points of intersection, which must be distinct. (b) If A is zero, the line is a tangent. For in this case i = 3-2, so that the points of intersection coincide. (c) If A is negative, the line does not meet the conic. For xi and 22 are imaginary, and hence there are no points of intersection (p. 77). If A = 0, one root of (1) is infinite (Theorem IV, p. 15) and one point of intersection is said to be " at infinity." If A = 0 and B-0, then both roots of ...
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Fine. Trade paperback (US). Glued binding. 444 p. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
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New. Trade paperback (US). Glued binding. 444 p. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
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Fine. Trade paperback (US). Glued binding. 444 p. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
