Problem

Identify the conic represented by \((x~-~1)^2~+~(y~+~3)^2~=~16\). State the standard-form feature that identifies it, then give its center and radius.

Big Picture

What this problem is really about

Identify the conic by matching its squared-term pattern to a standard form, then read its features from that same template. Shift coordinates appear with opposite signs inside their binomials, while a squared size parameter appears on the right. Keeping those two conventions separate prevents both the center-sign error and the mistake of reporting a squared measurement as a length.

Answer choices

Choose your path.

Preview only

This equation is a circle because both variables are squared, so the center is \((1,3)\) and the radius is 4.

This equation is a circle because it has the form \((x-h)^2+(y-k)^2=r^2\), so the center is \((1,-3)\) and the radius is 4.

This equation is a circle because it has the form \((x-h)^2+(y-k)^2=r^2\), so the center is \((-1,3)\) and the radius is 4.

This equation is a circle because it has the form \((x-h)^2+(y-k)^2=r^2\), so the center is \((1,-3)\) and the radius is 16.

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

Identify the conic represented by \((x~-~1)^2~+~(y~+~3)^2~=~16\). State the standard-form feature that identifies it, then give its center and radius.

What this problem is really about

Turn the preview into practice.

Gozunta lets you study this problem—and more than 10,000 others.