. College algebra, with applications. ) and (3) give us the general solution ofequation (1) in the case B ^ 0. If we substitute in themfor X any number whatever, and then compute the corre-sponding values of ?/, all pairs of numbers, x and i/, obtainedin this way are solutions of (1). EXERCISE CXI Solve each of the following equations for ?/ as a function of x and dis-cuss the following questions. Is the resulting function one-valued ortwo-valued ? If it is two-valued in general, are there any particularvalues of x for which the two values of y coincide? For what real valuesof X will the resul
. College algebra, with applications. ) and (3) give us the general solution ofequation (1) in the case B ^ 0. If we substitute in themfor X any number whatever, and then compute the corre-sponding values of ?/, all pairs of numbers, x and i/, obtainedin this way are solutions of (1). EXERCISE CXI Solve each of the following equations for ?/ as a function of x and dis-cuss the following questions. Is the resulting function one-valued ortwo-valued ? If it is two-valued in general, are there any particularvalues of x for which the two values of y coincide? For what real valuesof X will the resulting values of y also be real? 1. X- + _y2 = 4. 8. X- + if- = a^. 2. X- - y- = 4. 3. xy — 5. 4. 4x- -\- y^ = 10. 5. a,-2 + 4 7/2= 16. ^^- ~ ^ 11. 7. x^ - 4y- = 16. 18. (//- ^•)- = 4;>(.r-A). 19. {x - hy^ = ip(y - k). 20. (x - Ay + (y - iy = 5: ^^ (x -/,y _ (y - /.)- ^ ^ 21. (x - hy + (y - l-y = «2, • a-2 b- 24. _I:^^0_%^ = l. (r h- 25. - x2 -H 4 xy - ?/2 - 4 \/2 x + 2 V2 ^ - 11 = 0. 26. y^ - x^ - 6 X- 4- y - 3 X = Akt. 21:3] GRAPH OF QUADRATIC EQUATION 401 243. Graph of a function defined by a quadratic equation inX and y. Whenever a function, detinecl by means of a quad-ratic equation in x and y, is real, that is, if tlie quadraticequation has real solutions, these may be plotted as pointsin accordance witli the metliod which we have used so fre-quently. The general question as to the nature of thegraphs obtained in tins way, while not very dilTicult, isusually reserved for the course in analytic are, however, several special cases in which it is quiteeasy to draw the graphs. We shall now discuss some ofthese cases, a few of which have appeared already in thisbook in a different connection. Case 1. The graph of a quadratic equation in x and y con-sists of a pair of straight lines if the discriminant A is equal to zero. For we have seen in Art. 240 that, in this case, the quad-ratic function is a product of two linear functions, saya^T + b^g
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