Question

Which of the following equations will produce the graph shown below?

Answer 1

`6x^2 + 6y^2 = 144`, correctly represents a circle with a radius of 2√6. Other options depict an ellipse or circles with different radii. Option D is the correct choice.

The correct choice is D, represented by the equation which describes a circle. Step by step:

1. The given equation:
`6x^2 + 6y^2 = 144.`

2. Divide both sides by 6 to simplify:
`x^2 + y^2 = 24.`

3. Compare this with the general form of a circle equation:
`x^2 + y^2 = r^2,`where r is the radius.

4. Conclude that the circle has a radius of
`√(24) = 2√(6).`

5. Therefore, the equation
`6x^2 + 6y^2 = 144` indeed represents a circle with a radius of
`2√(6)`.

6. Eliminate other options: A (ellipse), B (circle with radius 5), and C (circle with radius 4) don't match the given equation.

In summary, option D correctly represents a circle with a radius of
`2√(6).`