. Algebraic geometry; a new treatise on analytical conic sections . PiQ. 92. 16a^ l&ac 16a , , m. FiQ. 93. .. from (1), _ 4V«i(ffl-ctan6)sin 6. tan 0 iV!5. If PQ cuts the curve asin the second figure, PK is stillequal to the algebraic differenceof the roots of the quadratic, forthe ordinate of Q is negative. 150. Infinite roofs of a quach-aticequation. Take the quadratic ax^ + bx + c = 0, (1) and let « = -, so that x = -.« y On substituting in (1), we have a b . or cy^ + by + a = 0 (2) Now if ffi = 0, one root of (2) is zero, one value of y is zero. 136 THE PAEABOLA. [chap. vni. Buta; = -
. Algebraic geometry; a new treatise on analytical conic sections . PiQ. 92. 16a^ l&ac 16a , , m. FiQ. 93. .. from (1), _ 4V«i(ffl-ctan6)sin 6. tan 0 iV!5. If PQ cuts the curve asin the second figure, PK is stillequal to the algebraic differenceof the roots of the quadratic, forthe ordinate of Q is negative. 150. Infinite roofs of a quach-aticequation. Take the quadratic ax^ + bx + c = 0, (1) and let « = -, so that x = -.« y On substituting in (1), we have a b . or cy^ + by + a = 0 (2) Now if ffi = 0, one root of (2) is zero, one value of y is zero. 136 THE PAEABOLA. [chap. vni. Buta; = -: .. wheny = 0, x — ^ = 0 .. if a = 0, one root of the quadratic ax^ + bx + c = 0 is other words, we may look upon the equation as a quadratic, one of whose roots is infinity. Again if a = 0 and S = 0, both roots of equation (2) are zero,and therefore both roots of equation (1) are infinity. Thus we may look upon the equation + ; + c = 0 as a quadratic, both of whose roots are may be seen in another we solve equation (1), ^^ -b±Jb^-iac2
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