Question

In a model, a submarine is located at point (0, 0) on the coordinate plane. The submarine’s radar range has an equation of 2x2 + 2y2 = 128

Draw the figure on a graph and label the location of the submarine. Make sure your name is on the paper, and label this activity Part 2.
Can the submarine’s radar detect a ship located at the point (6, 6) ? Mark that location on your graph, and explain how you know whether or not the ship will be detected in the space provided on the Circles Portfolio Worksheet.

Answer 1

Remember that for a circle centered in the point (a, b) and with a radius R, the equation is:

(x - a)^2 + (y - b)^2 = R^2

Here we know that the submarine is located at the point (0, 0)

And the radar range has the equation:

2*x^2 + 2*y^2 = 128

You can see that this seems like a circle equation.

If we divide both sides by 2, we get:

x^2 + y^2 = 128/2

x^2 + y^2 = 64 = 8^2

This is the equation for a circle centered in the point (0, 0) (which is the position of the submarine) of radius R = 8 units.

The graph can be seen below, this is just a circle of radius 8.

We also want to see if the submarine's radar can detect a ship located in the point (6, 6)

In the graph, this point is graphed, and you can see that it is outside the circle.

This means that it is outside the range of the radar, thus the radar can not detect the ship.