Write the equation in standard form for the circle with center (-8,-3) and radius 11

Answer 1

circles have the form (x-a)^2 + (y-b)^2 = r^2

a will shift the center of the circle left or right and b will shift the center of the circle up and down (in other words (a,b) is the center of the circle) while r is the radius. Therefore if we want the center of the circle at (-8,-3) we set a = -8 and b = -3 with radius 11 as r=11

so we get

(x+8)^2 + (y+3)^2 = 11^2 = 121

which can be seen by graphing it: https://www.desmos.com/calculator/hykyeotvwn

Answer 2

The standard form for the equation of a circle is:

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius of the circle.

The most common mistakes people make in this type of problem are:

*putting the wrong sign(s)

*forgetting to find r by taking the square root of r²

The left side of the equation deals with the center of the circle. In your problem, the center is (-8, -3),

so (x - h)² + (y - k)²

= (x - (-8))² + (y - (-3))².

When you simplify this expression, you get (x + 8)² + (y + 3)² . NOTICE how the signs changed because h and k are always SUBTRACTED.

When you simplify the expression, you subtract the negative numbers (-8 and -3), which is the same as adding positive numbers (+8 and +3).

The righthand side of the equation deals with the radius. They told us the radius is 11. So, now our equation becomes (x + 8)² + (y + 3)² = 11² .

Your teacher might want you to leave your answer this way or your teacher might want you to write your final answer as: (x + 8)² + (y + 3)² = 121.

NOTICE, the radius is NOT 121. The radius is √121.

In some problems, you will be given the equation and are asked to find the center and radius, so be sure you follow the steps above to see how these are related to the equation.