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Linear quadratic problem that the alternative solution

Have found that can curve equation and the equation of the curve point to solve the correspondence. For a straight line, the special point than the intersection of straight lines and axes, the following examples given by the solution of such problems, for your reference. Example 1 Prove: equation 3x a lOxy +3 y +9 x +5 a 12-0 that the two lines. Solution orders X 10, then the equation can be turned into a 12-0 3 +5,[link widoczny dla zalogowanych], solve for Y one by one 3, Y2 a ginger, so the curve 3 for a lOxy +3 y2 +9 x +5 points for a 12-0 must have A ( 0,[link widoczny dla zalogowanych], a 3 (0,[link widoczny dla zalogowanych], number). that Y 10,[link widoczny dla zalogowanych], then the equation can be reduced to a 12:0 3x2 +9 z, solve for Xl eleven 4, X2-1, so the curve of a lOxy +3 +9 +5 3x 12-0 will have a point C (a 4, O), D (1,0). If the equation of two straight lines, it should be a straight line AC and BD, or AD and BC. Linear AC's equation 3z +4 + 12-0, line BD in the equation 4z +3 a 4-0, the test is not true. line AD of the equation 3x-Y for a 3-0, linear equations for the X BC a 3y +4-0, formed by the inspection . In summary, the equation 3x a lOxy +3 y +9 z +5 a 12-0 that a two-line 3x-Y 3-0 and X a 3y +4-0. Example 2 k is a real number, if the equation X +-X + Y said the two lines of a 6-0, find the k value. Solutions that X 10,[link widoczny dla zalogowanych], was a 6 Y, then the curve X + kxy-X + Y over a 6-0 point A (0,6). ORDER Y a 0, then X. a X a 6-0,. '. X1-3, X2 2 one by one, then the curve X + kxy-X + a 6 a. through point B (3,0), C (a 2,0 ). If the equation X. +-X + Y a 6: == 0 means the two lines, there may be three situations: 1) two straight lines AB and AC, line AB of the equation 2z + Y a 6-0, linear AC of the equation 3z-Y +6 = 0, by inspection is not true. 2) There are two lines with the Y axis does not intersect a, i) two lines were X-3 and 3x-Y +6-0, not established by the test. ii) two lines one by one, respectively X 2 and 2z + Y a 6-0, by (z +2) (2x + Y a 6), 10 have 2x + xy a 12-0 for a 2x +2 y, and X + kxy-X + Y be a k-1 6-0 control 'can be seen from the above two cases, the form Ax + By + Cxy + Dx + Ey + F = O (A + B + C2 ≠ 0) that a straight line The problem, first find the intersection with the axis, just that z and Y, respectively, zero, and then get on the Y and z of the equation question (should pay particular attention the case of equation has a solution.) Find the intersection, the straight line equation obtained by the combination of authentication can be.