Question

Writing an Equation with a Given Center and Radius
Which equation represents a circle with a center at (2, -8) and a radius of 11?
(x - 3)2 + (y + 2)2 = 11
O (x - 2)2 + (y + 8)2 = 121
O (x + 2)2 + (y - 3)2 = 11
(x + 8)2 + (y – 2)2 = 121

Answer 1

Answer:

$(x-2)^2+(y+8)^2=121$

Step-by-step explanation:

A circle is described by an equation in the following form:

$(x-x_0)^2 + (y-y_0)^2 = r^2$ (1)

where:

$x_0$ is the x-coordinate of the centre of the circle

$y_0$ is the y-coordinate of the centre of the circle

r is the radius of the circle

For the circle in this problem, we have:

- The centre is located at (2,-8), so

$x_0=2\\y_0 = -8$

- The radius is 11, so

$r=11$

Therefore substituting into eq(1) we find the equation of this circle:

$(x-2)^2+(y+8)^2=11^2 = 121$

So the correct option is option B:

$(x-2)^2+(y+8)^2=121$

Answer 2

The equation represents a circle with a center at (2, -8) and a radius of 11 is (x-2)^2 + (y+8)^2= 121

Equation of a circle

The standard equation of a circle is expressed as:

(x-a)^2 + (y-b)^2= r^2

where"

(a, b) = (2, -8) is the centre

r is the radius = 11 units

Substitute

(x-2)^2 + (y-(-8))^2= 11^2

(x-2)^2 + (y+8)^2= 121

Hence the equation represents a circle with a center at (2, -8) and a radius of 11 is (x-2)^2 + (y+8)^2= 121

Learn more on equation of a circle here: https://brainly.com/question/1506955