Question

Draw the graph of the circle (x + 1)2 + (y + 4)2 = 4

Answer 1

Given the equation of the circle:

`(x+1)^2+(y+4)^2=4`

Let's draw a graph of the circle.

Apply the general equation of a circle:

`(x-h)^2+(y-k)^2=r^2`

Where:

(h, k) is the center of the circle.

r is the radius of the circle.

Rewrite 4 = 2²

Now, we have the equation:

`(x+1)^2+(y+4)^2=2^2`

Thus, we have the following:

Center of the circle: (h, k) ==> (-1, -4)

Radius of the circle = 2.

Since the radius is 2, let's find the four points around the circumference of the circle.

We have:

• Point by the right: (-1 +2, -4) ==> (1, -4)

,

• Point by the left: (-1 -2, -4) ==> (-3, -4)

,

• Point at the top: (-1, -4 + 2) ==> (-1, -2)

,

• Point at the bottom: (-1, -4 - 2) ==> (-1, -6)

Therefore, the graph of the circle will be:

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