Question

Consider a circle with its centre at the origin (O), as shown. Two operations are allowed on the circle.
Operation 1: Scale independently along the x and y axes.
Operation 2: Rotation in any direction about the origin.
Which figure among the options can be achieved through a combination of these two operations on the given circle?
\includegraphics[width=0.5\linewidth]{image2.png}

• A. A
• B. B
• C. C
• D. D

Hint:

When scaling a circle independently along the x and y axes, you get an ellipse. Rotation does not affect the shape, only the orientation.

Answer 1

The Correct Option is A

In this problem, we are allowed to scale the circle independently along the x and y axes (Operation 1). This scaling can distort the shape of the circle into an ellipse, depending on the scaling factors along each axis. Rotation about the origin (Operation 2) does not affect the general shape of the figure but merely changes its orientation.
- Option (A) shows an ellipse that results from scaling the circle along the x and y axes with different factors, and the figure is not rotated. Hence, this is a possible outcome of the operations.
- Option (B) shows a similar ellipse, but the orientation suggests that it might have been rotated differently, which is not possible without changing the scaling factors.
- Option (C) shows a figure that maintains the shape of a circle, which cannot be achieved through scaling alone.
- Option (D) shows an elongated oval shape, but this shape cannot result from a simple rotation of a circle or scaling along both axes in this manner.
Thus, the correct answer is (A).