A Treatise On the Principles And Applications of Analytic Geometry
A Treatise On the Principles And Applications of Analytic Geometry
Henry T Henry Turner Eddy
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This value of Xi in (g. ) gives r 2 ; and placing in equation (e. ) xi = 2 and r = 2, we find Also if we make y^ = and x l =4rm equation (e. ), we find Since a negative radius gives an imaginary circle, we can only use the upper sign of , or 0. 828 + ; whence a?i = 4 (V ^) = 5 . 172, or TANGENCIES OF LOCI, ETC. 87 Thus it appears that there are four circles which touch the three lines, as follows : O, l n, tf) ni O- / lV A Q . ** ^i *j yi r /V) ' 3d. ^-^-^v 7 ^, . Vi = 0, r = 2v'2 2; 4th. ^ = 6...- 226. Examples* (1. ) Find the equations of condition that the right line y mx + b may be tangent to the two circles Am. B = 2y'l + m\ and b = 6m (2. ) Find the resulting values of b and m. Ans. B = 12 or T 12 and m - (3. ) Show that the equations of the four lines which touch the two circles are yy-^5 = x + 12, and yy / ~ll = 5x 12, yy!$5 = x 12, and y j/77 = 5x + 12. Proposition 6'. T 227. TJieorem. The general equation of the n th degree- is. E. , an equation in which all the constants have general values can be made to fulfill | n(n + 3} conditions.
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