Find the radius of a circle with the equation
X^2+y^2-24x-32y+200= -791/4
a. 791/4
b. 9/4
c. 3/2
d. \sqrt{ }791/2
To find the radius of a circle from its equation in standard form, we can complete the square for both x and y.
Starting with the given equation:
x^2 + y^2 - 24x - 32y + 200 = -791/4
Rearranging the terms:
(x^2 - 24x) + (y^2 - 32y) = -791/4 - 200
Completing the square for the x and y terms:
(x^2 - 24x + 144) + (y^2 - 32y + 256) = -791/4 - 200 + 144 + 256
(x - 12)^2 + (y - 16)^2 = -791/4 + 200
(x - 12)^2 + (y - 16)^2 = -791/4 + 800/4
(x - 12)^2 + (y - 16)^2 = 9/4
Now, we can see that the equation is in the standard form of a circle:
(x - h)^2 + (y - k)^2 = r^2, where (h,k) is the center of the circle and r is the radius.
Comparing this equation to the standard form, we can see that the radius squared is 9/4. Therefore, the radius of the circle is:
r = sqrt(9/4)
r = 3/2
Therefore, the correct answer is:
c. 3/2