Witing the equation of a circle centered at the origin given its radius or a... Give the equation of the circle centered at the origin and passing through the point $$ (0,10) $$.

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To find the equation of a circle centered at the origin with a given radius, we can use the standard form of the equation of a circle:

$$
x^2 + y^2 = r^2
$$

where $$ (h, k) $$ is the center of the circle and $$ r $$ is the radius. Since the circle is centered at the origin, $$ h = 0 $$ and $$ k = 0 $$.

Given that the circle passes through the point $$ (0, 10) $$, we can determine the radius $$ r $$ by calculating the distance from the center (the origin) to the point $$ (0, 10) $$. The distance is simply the y-coordinate of the point since the x-coordinate is 0.

Thus, the radius $$ r $$ is:

$$
r = 10
$$

Now, we can substitute $$ r $$ into the equation of the circle:

$$
x^2 + y^2 = 10^2
$$

This simplifies to:

$$
x^2 + y^2 = 100
$$

So, the equation of the circle centered at the origin and passing through the point $$ (0, 10) $$ is:

$$
x^2 + y^2 = 100
$$
The equation of the circle centered at the origin and passing through the point $$ (0, 10) $$ is: $$ x^2 + y^2 = 100 $$

Witing the equation of a circle centered at the origin given its radius or a... Give the equation of the circle centered at the origin and passing through the point \( (0,10) \).

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