Question

Match each equation to its description

A.Circle centered at (0,-4) with radius of 3
1.(x-1)^2 + y^2=9
2.x^2+(y+4)^2=9
3. (x-1) +( y - 4)^2=3
4.(x - 1)^2+(y - 4)^2=9
5.(x - 1)^2 + (y + 4)^2=3
Which is the correct answer
A.1
B.2
C.3
D.4
E.5

Answer 1

`\boxed {\boxed {\sf B. \ 2: x^2+(y+4)^2=9}}}`

Explanation:

The equation for a circle is:

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

Where (h, k) is the center and r is the radius.

We know that the center of the circle is (0, -4) and the radius is 3. Therefore:

• h= 0
• y= -4
• r=3

Substitute the values into the formula.

`(x-0)^2+(y--4)^2=(3)^2`

Solve the first parentheses.

• (x-0)² = (x)²= x²

`x^2+(y--4)^2=(3)^2`

Solve the next parentheses.

• (y--4)² = (y+4)²

`x^2+(y+4)^2=(3)^2`

Solve the exponent.

• (3)²= 3*3=9

`x^2+(y+4)^2=9`

This is the finished equation, which corresponds with number 2. Choice B (2): x²+(y+4)²= 9 is correct.