Respuesta :

gustanika
Find the radius (or you can find the square of the radius)
the general equation for a circle is
(x - a)² + (y - b)² = r²
with (a,b) as the center, and (x,y) is one of the points

plug in the numbers to the equation to find the value of r
(x - a)² + (y - b)² = r²
(5 - 2)² + (0 - (-3))² = r²
3² + (0 + 3)² = r²
3² + 3² = r²
2(3²) = r²
r² = 2(3²)
r² = 2(9)
r² = 18

Find the area of the circle
a = π × r²
a = 3,14 × 18
a = 56.52

The area of the circle is 56.52 square unit

Answer: 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

[tex]A=\pi r^2.[/tex]

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

[tex](x-h)^2+(y-k)^2=r^2~~~~~~~~~~~~~~~~(i)[/tex]

For the given circle, we have

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

[tex](x-2)^2+(y+3)^2=r^2.[/tex]

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

[tex](5-2)^2+(0+3)^2=r^2\\\\\Rightarrow r^2=3^3+3^2\\\\\Rightarrow r^2=18\\\\\Rightarrow r=3\sqrt2.[/tex]

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

Therefore, the area of the circle will be

[tex]A\\\\=\pi r^2\\\\=\dfrac{22}{7}\times (3\sqrt2)^2\\\\=\dfrac{22}{7}\times 18\\\\=56.57~\textup{sq. units.}[/tex]

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

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