How to find domain and range from the equation (x+6)^2+(y+4)^2=16

Question

I can find the center and radius but I am lost on how to find the domain and range.

Answer 1

Hi Elizabeth,

So you know the center is (-6, -4) and you know the radius is 4. Domain means all possible values for x and range means all possible values for y. For a circle with radius 4, the domain is everything within 4 units of -6. So:

Domain= (-10, -2)

Now, for the range, we want everything within 4 units of -4. So the range is:

Range: (-8,0)

I hope this helps.

Answer 2

So, clearly this is the equation of a circle. Knowing that we can pull necessary information from the equation about this particular circle.

Since we have + signs in each set of parentheses instead of - signs, that indicates that the x and y values for the center will both be negative.

The center is, therefore. (-6, -4).

On the right side of the equal sign is 16, telling us that the radius is the square root of 16, which is 4.

Sstarting at the center, go 4 units left and 4 units right, giving us 2 points on the circle:

(-10, -4) & (-2, -4)

You can also move 4 units up and 4 units down from the center giving us 2 additional points on the circle: (-6, 0) & (-6, -8). Draw the circle.

The domain is the list of x values. All values between -10 and -2 including -10 and -2.