Question

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

Answer 1

Answer:

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

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).