In standard (x,y )coordinate plane,the graph of (x-2)^2 + (y+4)^2=9 is a circle.What is the area enclosed by this circle,expressed in square coordinate units?
The area enclosed by the circle is approximately 50.265 square coordinate units.
Well, well, well, a circle, huh? Circle, circle, round and round we go! To find the area of a circle, we need to use a little math magic.
Here's the deal: the equation (x - 2)^2 + (y + 4)^2 = 9 tells us that the circle has a radius of 3 units. Remember that the formula to find the area of a circle is πr², where π is approximately 3.14159 and r is the radius.
So, plug that value in, and we get the area of this circle to be approximately 3.14159 * 3² = 3.14159 * 9 = 28.27 square coordinate units.
Voila! The area enclosed by this circle is approximately 28.27 square coordinate units. Keep those circles rolling!
To find the area enclosed by the circle equation (x-2)^2 + (y+4)^2 = 9, we first recognize that the equation is of the form (x-h)^2 + (y-k)^2 = r^2, where (h,k) represents the center of the circle, and r represents the radius.
Comparing the given equation with the standard form, we can identify that the center of the circle (h, k) is (2, -4), and the radius (r) is √9 = 3.
The area enclosed by a circle can be calculated using the formula A = πr^2, where A represents the area and r represents the radius.
Plugging in the values, we have A = π(3)^2 = π(9) = 9π.
Therefore, the area enclosed by the given circle is 9π square coordinate units.
To find the area enclosed by the circle given by the equation (x - 2)^2 + (y + 4)^2 = 9, we need to determine the radius of the circle.
The equation of a circle in standard form is (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center of the circle and r represents the radius. By comparing this standard form with the given equation, we can see that the center of the circle is (2, -4) and the radius is √9 = 3.
The formula to calculate the area of a circle is A = πr^2, where A represents the area and r represents the radius. Now that we know the radius is 3, we can substitute it into the formula to find the area:
A = π(3)^2
= π(9)
= 9π
Therefore, the area enclosed by the circle is 9π square coordinate units.