Question

Identify the center of the circle defined by the equation (x + 4)² + (y - 1)² = 32

Answer 1

The centre of the circle is (-4,1).

Step-by-step explanation

Given the equation of the circle:

`\mleft(x+4\mright)^2+(y-1)^2=32`

Comparing with the standard form of the equation of a circle:

`\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ Where\; Centre=(h,k) \end{gathered}`

We see that:

`\begin{gathered} x-h=x+4 \\ \implies h=-4 \\ \text{Also:} \\ y-k=y-1 \\ \implies k=1 \end{gathered}`

The centre of the circle is (-4,1).