In the graph of a circle, moving (x-h) to the right indicates what?

In the graph of a circle, moving (x-h) to the right indicates what?

• A. Vertical translation
• B. Horizontal translation left
• C. Horizontal translation right
• D. Scaling of the circle

Answer: (C)

In the context of the equation of a circle, which is typically written in the standard form \((x-h)^2 + (y-k)^2 = r^2\), the terms \(h\) and \(k\) represent the center of the circle at the coordinates \((h, k)\). When considering the expression \((x-h)\), moving it to the right actually means that the value of \(h\) is decreasing, which results in an increase in the x-coordinate of the center point as we adjust \(x\) in the graph. This corresponds to a horizontal translation of the entire graph of the circle to the right. In simpler terms, if you increase the value of \(h\) (by taking \(h\) to a larger number), the graph shifts left; conversely, if you decrease \(h\), the graph shifts to the right. Thus, when we specifically focus on the effect of moving \((x-h)\) to the right, it indicates a shift of the circle's center along the x-axis in the positive direction, confirming that it is a horizontal translation to the right.

In the context of the equation of a circle, which is typically written in the standard form ((x-h)^2 + (y-k)^2 = r^2), the terms (h) and (k) represent the center of the circle at the coordinates ((h, k)).

When considering the expression ((x-h)), moving it to the right actually means that the value of (h) is decreasing, which results in an increase in the x-coordinate of the center point as we adjust (x) in the graph. This corresponds to a horizontal translation of the entire graph of the circle to the right.

In simpler terms, if you increase the value of (h) (by taking (h) to a larger number), the graph shifts left; conversely, if you decrease (h), the graph shifts to the right. Thus, when we specifically focus on the effect of moving ((x-h)) to the right, it indicates a shift of the circle's center along the x-axis in the positive direction, confirming that it is a horizontal translation to the right.