Question

46. Identify the center and radius of a circle given the equation is (x - 2)^2 + (y + 4)^2= 36

Answer 1

Answer: Center: (2, –4); Radius: 6.

Step-by-step explanation

The equation of a circle in standard form is:

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

where (h, k) is the center and r is the radius. Thus, in our given equation:

`\left(x-2\right)^2+(y+4)^2=36`

• h = 2

,

• k = –4 (it is negative as negative sign times negative sign equals positive sign)

,

• r² = 36

Therefore, the center is (2, –4) and the radius is:

`r^2=36`
`√(r^2)=√(36)`
`r=6`