An Elementary Treatise On Conic Sections And Algebraic Geometry With Numerous
An Elementary Treatise On Conic Sections And Algebraic Geometry With Numerous
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In our eReader you can find the full English version of the book. Read An Elementary Treatise On Conic Sections And Algebraic Geometry With Numerous 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 An Elementary Treatise On Conic Sections And Algebraic Geometry With Numerous
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To quickly assess the difficulty of the text, read a short excerpt:
121; then, if we suppose (x y ) to be on the circle, so that x 2 + 7/ 2 = r 3, the equation becomes ?/ 2 M 2 + 2x y m + x * = 0, or my + x = ; hence /j. And fj. Are each equal to -, , and equations (2) of Art. 121 become since the tangents which can be drawn from (x y ) now coincide.
121. To determine the equations to the tangents drawn to a circle from any point (x y).
Let the equation to the tangent be y mx = + rjl + m 2 ; THE TANGENT. 125 then, since it passes through (xy), the co-ordinates ...of that point satisfy the equation, and we have (if - mx) z = r 2 (1 + ra 2 ), or (x* - r 2 ) m* - Zxy m + y z - r 2 = (1), a quadratic to determine the two values of m, in the equa tions to the two tangents which can be drawn to the circle from (xy). If p and /* be the two roots, the required equations will be (Art. 29, Cor. 1) y-y = n(x-x), y-y =^ (x-x) (2).
COR. Solving equation (1), we have y r Jx* + y - r 2 whence we see that the values of ra are real, if # 2 + y* > ?- 2, or the point is outside the circle; they are equal, when x l + ?/ 2 = r 2, or the point is on the circle ; and they are imaginary, when x* -f- y" 2
What to read after An Elementary Treatise On Conic Sections And Algebraic Geometry With Numerous?
You can find similar books in the "Read Also" column, or choose other free books by G Hale George Hale Puckle to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
121; then, if we suppose (x y ) to be on the circle, so that x 2 + 7/ 2 = r 3, the equation becomes ?/ 2 M 2 + 2x y m + x * = 0, or my + x = ; hence /j. And fj. Are each equal to -, , and equations (2) of Art. 121 become since the tangents which can be drawn from (x y ) now coincide.
121. To determine the equations to the tangents drawn to a circle from any point (x y).
Let the equation to the tangent be y mx = + rjl + m 2 ; THE TANGENT. 125 then, since it passes through (xy), the co-ordinates ...of that point satisfy the equation, and we have (if - mx) z = r 2 (1 + ra 2 ), or (x* - r 2 ) m* - Zxy m + y z - r 2 = (1), a quadratic to determine the two values of m, in the equa tions to the two tangents which can be drawn to the circle from (xy). If p and /* be the two roots, the required equations will be (Art. 29, Cor. 1) y-y = n(x-x), y-y =^ (x-x) (2).
COR. Solving equation (1), we have y r Jx* + y - r 2 whence we see that the values of ra are real, if # 2 + y* > ?- 2, or the point is outside the circle; they are equal, when x l + ?/ 2 = r 2, or the point is on the circle ; and they are imaginary, when x* -f- y" 2
What to read after An Elementary Treatise On Conic Sections And Algebraic Geometry With Numerous?
You can find similar books in the "Read Also" column, or choose other free books by G Hale George Hale Puckle to read onlineMoreLess
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