The given equation is $y^2 + x^2 = 9$. This represents a circle centered at the origin with a radius of 3.

We need to find the corresponding $y$ values for the given $x$ values: $x = 2, 1, 0, -1, -2$.

Steps:

1. Substitute each $x$ value into the equation and solve for $y$.

For $x = 2$:

$y^2 + 2^2 = 9$ $y^2 + 4 = 9$ $y^2 = 5$ $y = \pm \sqrt{5}$

For $x = 1$:

$y^2 + 1^2 = 9$ $y^2 + 1 = 9$ $y^2 = 8$ $y = \pm \sqrt{8} = \pm 2\sqrt{2}$

For $x = 0$:

$y^2 + 0^2 = 9$ $y^2 = 9$ $y = \pm 3$

For $x = -1$:

$y^2 + (-1)^2 = 9$ $y^2 + 1 = 9$ $y^2 = 8$ $y = \pm \sqrt{8} = \pm 2\sqrt{2}$

For $x = -2$:

$y^2 + (-2)^2 = 9$ $y^2 + 4 = 9$ $y^2 = 5$ $y = \pm \sqrt{5}$

Results:

• $x = 2$: $y = \pm \sqrt{5}$
• $x = 1$: $y = \pm 2\sqrt{2}$
• $x = 0$: $y = \pm 3$
• $x = -1$: $y = \pm 2\sqrt{2}$
• $x = -2$: $y = \pm \sqrt{5}$

Would you like any details or have any questions?

Related Questions:

1. What is the general form of a circle equation?
2. How do you derive the radius of a circle from its equation?
3. Can the equation of a circle be transformed into another form?
4. What are the properties of the circle centered at the origin?
5. How do you determine if a point lies on a circle?
6. How do you find the distance between two points on a circle?
7. How can you use the Pythagorean theorem to solve circle-related problems?
8. What are the differences between the equations of a circle and an ellipse?

Tip:

When dealing with equations of a circle, remember that every point on the circle is equidistant from the center, which helps in solving for variables when given specific points.