SOLUTION: Suppose that y = −3/x and xy + 9 = 0 are equations that define two different hyperbolas. The line defined by x+y = 0 cuts each of the hyperbolas twice, at the points A and B (for

Question 1142383: Suppose that y = −3/x and xy + 9 = 0 are equations that define two different hyperbolas. The line defined by x+y = 0 cuts each of the hyperbolas twice, at the points A and B (for y = −3/x) and C and D (for xy + 9 = 0). A and C are in the same quadrant; B and D are both in the quadrant opposite A and C.
Which of the following statements is/are true?
A. The hyperbolas have no points of intersection.
B. The hyperbolas both lie in quadrants 2 and 4.
C. The ratio of the x - coordinate of A to the x - coordinate of C is sqrt3/3.
1. Only A
2. Only B
3. Only C
4. Only A and B
5. A, B and C

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

The equations are equivalent to y = -3/x and y = -9/x.

Statement A: To see if there are any points of intersection, see what happens when you try to solve the pair of equations simultaneously.
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Statement B: If this is true, then x negative makes y positive (quadrant 2) and x positive makes y negative (quadrant 4). Do these equations have that property?

Statement C: To see if this is true, choose a simple value for x (1 is nearly always a good choice) and see what the resulting y values are.
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