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Question at position 22
Which of the following is a result of shifting a circle with equation (x + 3)² + (y - 2)² = 36 right 3 units?

Answer 1

To shift the circle represented by the equation \((x + 3)^2 + (y - 2)^2 = 36\) right 3 units, you would modify the \(x\) term in the equation.

The original equation is in the form \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center of the circle and \(r\) is the radius.

The center of the original circle at \((h, k)\) is \((-3, 2)\) and the radius \(r\) is \(\sqrt{36} = 6\).

Shifting the circle right 3 units involves adding 3 to the \(x\) coordinate of the center:

\[
h = -3 + 3 = 0
\]

So, the new center after the shift will be at \((0, 2)\).

The new equation of the circle after the shift becomes:

\[
(x - 0)^2 + (y - 2)^2 = 36
\]

or simply:

\[
x^2 + (y - 2)^2 = 36
\]

So, the result of shifting the circle right 3 units is:

**\(x^2 + (y - 2)^2 = 36\)**