Question

draw the circle $(x + 1)^2+(y + 2)^2 = 16$.

Explanation:

Step1: Find the center of the circle

The standard form of a circle is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center.
For the circle \((x + 1)^2+(y + 2)^2=16\), we have \(h=-1,k = - 2\). So the center is \((-1,-2)\).

Step2: Find the radius of the circle

Since \(r^2 = 16\), then \(r=\sqrt{16}=4\).

Step3: Plot the circle

• Plot the center \((-1,-2)\) on the coordinate plane.
• From the center, move 4 units up, down, left and right. The points will be \((-1,-2 + 4)=(-1,2)\), \((-1,-2-4)=(-1,-6)\), \((-1 - 4,-2)=(-5,-2)\) and \((-1+4,-2)=(3,-2)\).
• Sketch the circle passing through these four points.

Answer:

Plot the center at \((-1,-2)\) and draw a circle with radius \(4\) units.