An Elementary Treatise On Conic Sections And Algebraic Geometry With Numerous

G Hale George Hale Puckle

The book An Elementary Treatise On Conic Sections And Algebraic Geometry With Numerous was written by author G Hale George Hale Puckle Here you can read free online of An Elementary Treatise On Conic Sections And Algebraic Geometry With Numerous book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is An Elementary Treatise On Conic Sections And Algebraic Geometry With Numerous a good or bad book?

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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

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