Question

A circle with the equation ( x + 3) 2 + ( y - 2) 2 = 25 is reflected over the line x = 2.

What is the equation of the image?

A. ( x - 3) 2 + ( y + 2) 2 = 25
B. ( x - 7) 2 + ( y - 2) 2 = 25
C. ( x - 7) 2 + ( y + 2) 2 = 25
D. ( x - 3) 2 + ( y - 2) 2 = 25

Answer 1

Answer: A

Explanation:

To find the equation of the image after reflecting the circle over the line x = 2, we need to make the following transformation:

Reflect the x-coordinate of each point of the original circle with respect to the line x = 2.

The equation of the original circle is (x + 3)^2 + (y - 2)^2 = 25.

The line x = 2 is a vertical line passing through x = 2. When we reflect a point over this line, the x-coordinate of the point changes sign while the y-coordinate remains the same.

So, after reflecting, the x-coordinate (x + 3) of the original circle becomes (x - 3), and the y-coordinate (y - 2) remains the same.

Thus, the equation of the reflected circle is: (x - 3)^2 + (y - 2)^2 = 25.

The correct answer is option A: (x - 3)2 + (y - 2)2 = 25.