Here's why:
* Standard Form: The standard form of the equation of a circle is:
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle and r is the radius.
* Horizontal Shift: When you shift the circle horizontally, you are essentially changing the value of 'h'.
* Example:
* A circle centered at (2, 3) with radius 5 has the equation: (x - 2)² + (y - 3)² = 25
* If you shift this circle 4 units to the right, the new center is (6, 3), and the equation becomes: (x - 6)² + (y - 3)² = 25
Key Point: Notice that only the 'h' value changed, representing the horizontal shift.
