Question

Which of the following is a result of shifting a circle with equation

(x - 2)2 + (y - 3)2 = 25

up 2 units?

  A. Both the x- and y-coordinates of the center of the circle decrease by 2.
  B. The x-coordinate of the center of the circle increases by 2.
  C. Both the x- and y-coordinates of the center of the circle increase by 2.
  D. The y-coordinate of the center of the circle increases by 2.

Answer 1

The center of the circle will have the same x coordinate but the y coordinate will increase by 2,.

Answer is D

Answer 2

Option D - The y-coordinate of the center of the circle increases by 2.

Explanation:

Given : Shifting a circle with equation
`(x - 2)^2 + (y - 3)^2 = 25` up 2 units.

To find : Which of the following is a result of shifting ?

Solution :

The given equation is
`(x - 2)^2 + (y - 3)^2 = 25`

Since, the circle is shifted up 2 units i.e. (2,3)→(2,4)

There will be no change in x-axis because it is vertical change.

So, Option A,B and C are discarded.

Therefore, Option D is correct.

The y-coordinate of the center of the circle increases by 2.