Let the equation of a circle be x^2+y^2-14x+8y+56


a. Find the standard form of the circle
b. Find the center of the circle
c. Find the radius of the circle

Equation of the circle in standard form

Help me please

Find the coordinate of the centre and the radius of the circle

x2+y2-14x-8y+56=0

a. To find the standard form of the circle, we complete the square for both x and y terms. First, let's group the x and y terms together:

(x^2 - 14x) + (y^2 + 8y) + 56 = 0

To complete the square for x, we need to add (14/2)^2 = 49 to both sides:

(x^2 - 14x + 49) + (y^2 + 8y) + 56 = 49

For y, we add (8/2)^2 = 16 to both sides:

(x^2 - 14x + 49) + (y^2 + 8y + 16) + 56 = 49 + 16

Simplifying, we have:

(x - 7)^2 + (y + 4)^2 = 9

So, the standard form of the circle is:

(x - 7)^2 + (y + 4)^2 = 9

b. To find the center of the circle, we look at the equation in standard form. The center of the circle is given by the values inside the parentheses. Therefore, the center is (7, -4).

c. To find the radius of the circle, we look at the equation in standard form. The radius is the square root of the constant term on the right-hand side. In this case, the radius is √9 = 3. So, the radius is 3.

To find the standard form of the circle, we need to rewrite the equation in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center of the circle and r represents the radius.

a. Standard form of the circle:
Start by completing the square for the x and y terms:

x^2 - 14x + y^2 + 8y = -56

To complete the square for the x terms, take half of the coefficient of x (-14) and square it: (-14/2)^2 = 49.
Add 49 to both sides of the equation:

x^2 - 14x + 49 + y^2 + 8y = -56 + 49

Now, complete the square for the y terms in the same way.
Take half of the coefficient of y (8) and square it: (8/2)^2 = 16.
Add 16 to both sides of the equation:

x^2 - 14x + 49 + y^2 + 8y + 16 = -56 + 49 + 16

Simplify:

(x^2 - 14x + 49) + (y^2 + 8y + 16) = 9

Now, rewrite the equation as a perfect square trinomial for both x and y:

(x - 7)^2 + (y + 4)^2 = 9

Therefore, the standard form of the circle is (x - 7)^2 + (y + 4)^2 = 9.

b. Center of the circle:
In the standard form, the equation (x - h)^2 + (y - k)^2 = r^2 represents a circle with center (h, k). Thus, the center of the circle is (7, -4).

c. Radius of the circle:
In the standard form, the equation (x - h)^2 + (y - k)^2 = r^2 represents a circle with radius r. By comparing the equation to the standard form, we can see that the radius squared is 9. This means the radius itself is 3.

Therefore, the radius of the circle is 3.