Question

What is the area of the circle described by the equation X to the second- degree plus(Y +1/5) to the second degree equals 9/25

Answer 1

The equation of the circle given is:

\[
x^2 + \left(y + \frac{1}{5}\right)^2 = \frac{9}{25}
\]

This is in the standard form of a circle, which is:

\[
(x - h)^2 + (y - k)^2 = r^2
\]

where \((h, k)\) is the center of the circle, and \(r\) is the radius.

From the given equation:

1. \(h = 0\)
2. \(k = -\frac{1}{5}\)
3. \(r^2 = \frac{9}{25}\)

To find the radius \(r\), we take the square root of \(r^2\):

\[
r = \sqrt{\frac{9}{25}} = \frac{3}{5}
\]

Now, the area \(A\) of a circle is given by the formula:

\[
A = \pi r^2
\]

Substituting \(r^2 = \frac{9}{25}\) into the area formula:

\[
A = \pi \left(\frac{9}{25}\right) = \frac{9\pi}{25}
\]

Thus, the area of the circle is:

\[
\frac{9\pi}{25}
\]