Find the center and radius of the given circle and graph it.
1. x^2+y^2+10+21=0
you must have a typo
x^2 + y^2 = -31
not possible for a circle.
are you sure it wasn't 10x ?
Yes. it Was 10x ..
To determine the center and radius of a circle with the equation x^2 + y^2 + 10x + 21 = 0, we can rewrite it in the standard form (x - h)^2 + (y - k)^2 = r^2.
Step 1: Separate the x and y terms from the constant terms:
x^2 + y^2 + 10x + 21 = 0
(x^2 + 10x) + (y^2) = -21
Step 2: Complete the square for the x terms:
Take half of the coefficient of x (which is 10) and square it: (10/2)^2 = 25
Add this value to both sides of the equation:
(x^2 + 10x + 25) + y^2 = -21 + 25
(x + 5)^2 + y^2 = 4
Step 3: Rewrite the equation in standard form:
(x + 5)^2 + y^2 = 4
(x - (-5))^2 + (y - 0)^2 = 2^2
Comparing this with the standard equation (x - h)^2 + (y - k)^2 = r^2, we can determine the center and radius:
Center: (-h, -k) = (-(-5), 0) = (5, 0)
Radius: r = sqrt(r^2) = sqrt(2^2) = 2
Therefore, the center of the circle is (5, 0) and the radius is 2. To graph it, plot the center point at (5, 0) and draw a circle with a radius of 2.