Discussion
The following (X, Y) points are plotted on X-Y plane and the adjacent points are joined by smooth curve :
| X | Y |
|---|---|
| 1 | 60 |
| 2 | 30 |
| 3 | 20 |
| 4 | 15 |
| 5 | 12 |
What will be the nature of curve ?
Answer: C
The curve is a Hyperbola.
For every point the product XY is the same: 1 x 60 = 2 x 30 = 3 x 20 = 4 x 15 = 5 x 12 = 60. So the points lie on XY = 60, that is \(Y = \frac{60}{X}\), a rectangular hyperbola: Y is inversely proportional to X.
A straight line needs equal changes in Y for equal steps in X (here they are 30, 10, 5, 3). Y falls but not by a constant ratio (30/60 = 0.5, 20/30 = 0.67), so it is not exponential, and a parabola would turn upward again.
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