Coordinate Geometry
Coordinate Geometry
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In our eReader you can find the full English version of the book. Read Coordinate Geometry Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Coordinate Geometry
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To quickly assess the difficulty of the text, read a short excerpt:
In the conic q^/g? -|- 2^/6* = 1 (1), where a>6, the foci are on the o^axis and at the distance ae = a Vl — h^/a^ = Va* — 6* to the right and left of the origin.
Let A denote an arbitrary constant ; then the equation a* + X. ^b*+\ (2) will represent the system of conies which have the same foci as the conic (1) ; for in any conic (2) the distance from the center to a focus is } (a* + A) — (b^ + ^)lK ^^at is, Va* — b^.
167. For all positive values of A., and all negative values between and — 6*,... both a* + A and 6' 4- A are positive, and (2) therefore represents ellipses ; for all values of A between — 6* and —a*, a*-|-A is positive, and 6*-hA is negative, and (2) therefore represents hyperbolas; for all values of A between — a* and — 00 , both a' + A and 6* -|- A are negative, and the locus of (2) is therefore imaginary.
SYSTEMS OF CONICS 145 168. Through every point («', y') there pass two conies of the system (2), the one being an eUipse, the other an hyperbola.
For substitute (a?', y') for (x, y) in (2), and clear of fractions ; the result is (A + a2)(X + W) - x\\ + b^) - J/^CX + a^ = 0.
What to read after Coordinate Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Henry B Henry Burchard Fine to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
In the conic q^/g? -|- 2^/6* = 1 (1), where a>6, the foci are on the o^axis and at the distance ae = a Vl — h^/a^ = Va* — 6* to the right and left of the origin.
Let A denote an arbitrary constant ; then the equation a* + X. ^b*+\ (2) will represent the system of conies which have the same foci as the conic (1) ; for in any conic (2) the distance from the center to a focus is } (a* + A) — (b^ + ^)lK ^^at is, Va* — b^.
167. For all positive values of A., and all negative values between and — 6*,... both a* + A and 6' 4- A are positive, and (2) therefore represents ellipses ; for all values of A between — 6* and —a*, a*-|-A is positive, and 6*-hA is negative, and (2) therefore represents hyperbolas; for all values of A between — a* and — 00 , both a' + A and 6* -|- A are negative, and the locus of (2) is therefore imaginary.
SYSTEMS OF CONICS 145 168. Through every point («', y') there pass two conies of the system (2), the one being an eUipse, the other an hyperbola.
For substitute (a?', y') for (x, y) in (2), and clear of fractions ; the result is (A + a2)(X + W) - x\\ + b^) - J/^CX + a^ = 0.
What to read after Coordinate Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Henry B Henry Burchard Fine to read onlineMoreLess
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