Question

Question content area top Part 1 A system for tracking ships indicates that a ship lies on a path described by 2y2−x2=1. The process is repeated and the ship is found to lie on a path described by 3x2−y2=2. If it is known that the ship is located in the first quadrant of the coordinate​ system, determine its exact location.

Answer 1

The exact coordinate location of the ship is: (1, 1)

How to find the location coordinates?

In the first test, the equation of the position was:

2y² - x² = 1 ...........> equation I

In the second test, the equation of the position was:

3x² - y² = 2 ..............> equation II

This equation can be rewritten as:

y² = 3x² - 2 ............> equation III

Since the ship did not move in the duration between the two tests, therefore, the position of the ship is the same in the two tests which means that:

equation I = equation II

To get the position of the ship, we will simply need to solve equation I and equation II simultaneously and get their solution.

Substitute with equation III in equation I to solve for x as follows:

2(3x² - 2) - x² = 1

6x² - 4 - x² = 1

5x² = 5

x² = 5/5 = 1

x = ± √1

We are given that the ship lies in the first quadrant. This means that both its x and y coordinates are positive. This means that:

x = 1

Substitute with x in equation III to get y as follows:

y² = 3(1)² - 2

y² = 1

y = +√1

y = 1

Based on the above, the position of the ship is (1, 1).