SOLUTION: Suppose the function f is defined by 2xy − 25 = 0. Which of the following statements is / are true? A. The graph of f is a hyperbola which lies in the first and third qu

Algebra ->  Formulas -> SOLUTION: Suppose the function f is defined by 2xy − 25 = 0. Which of the following statements is / are true? A. The graph of f is a hyperbola which lies in the first and third qu      Log On


   

Question 1142382: Suppose the function f is defined by
2xy − 25 = 0.
Which of the following statements is / are true?
A. The graph of f is a hyperbola which lies in the first and third quadrants.
B. The shortest distance from the origin to a point on the graph of f is 5 units.
C. The line defined by y = x cuts the graph of f in two points.
1. Only A
2. Only B
3. Only C
4. Only A and B
5. A, B and C
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The function is equivalent to xy = 25/2.

Statement A: True if x positive makes y positive also and x negative makes y negative also. Is that true about this function?

Statement B: This will be easier after you look at statement C.

Statement C: True if the system of equations xy=25/2 and y=x has two solutions.

xy+=+25%2F2 --> x%5E2+=+25%2F2 (because y=x) --> x+=+5%2Fsqrt%282%29 or x+=+-5%2Fsqrt%282%29

Back to Statement B: Because the equation is symmetric in x and y (exchanging the two variables produces the same equation), the graph is symmetric about the line y=x. That means the shortest distance from the origin to a point on the graph is the distance to one of the two points found in working on Statement C. A simple application of the distance formula will give you that distance.