Question

Consider the equation of a circle. x2+y2+2x−2y−7=0 Select all true statements.

Answer 1

The equation of the circle can be written in standard form as:

(x + 1)² + (y - 1)² = 9

Therefore, the center of the circle is at (-1, 1) and the radius is 3.

Now, let's look at the statements:

1. The center of the circle is (-2, 1).
2. False. The center of the circle is (-1, 1).
3. The radius of the circle is 2.
4. False. The radius of the circle is 3.
5. The circle intersects the y-axis at (0, 4) and (0, -2).
6. False. The circle does not intersect the y-axis.
7. The circle intersects the x-axis at (-4, 0) and (2, 0).
8. False. The circle does not intersect the x-axis.
9. The area of the circle is 9π.
10. False. The area of the circle is 9π.

Therefore, the only true statement is:

• The center of the circle is (-1, 1).