In the coordinate plane, a circle has center (2,−3) and passes through the point (5,0). what is the area of the circle?

The area of the circle is 56.57 sq. units.

Step-by-step explanation:  We are given to find the area of a circle that has center (2, -3) and passes through the point (5, 0).

We know that the area of a circle with radius 'r' units is given by

The standard equation of a circle with center (h, k) and radius 'r' units is given by

For the given circle, we have

center, (h, k) = (2, -3). So, equation (i) becomes

Since the circle passes through the point (5, 0), so we get

So, the radius of the circle is 3√2 units.

Therefore, the area of the circle will be

Thus, the area of the circle is 56.57 sq. units.