Question

What is the equation for the translation of x2 + y2 = 25 two units to the left and four units down? (x – 2)2 + (y – 4)2 = 25 (x – 2)2 + (y + 4)2 = 25 (x + 2)2 + (y + 4)2 = 25 (x + 2)2 + (y – 4)2 = 25 description?

Answer 1

move down c units means add c to every y
move left c units means add c to every x
so
move 2 left and 4 down means
add 2 to every x and add 4 to every y
so
(x+2)²+(y+4)²=25

3rd one

Answer 2

D.
`(x+2)^2+(y-4)^2=25`

Explanation:

We have been given an equation
`x^2+y^2=25`. We are asked to find the equation after a translation of two units to the left and four units down.

We know that translation of two units to the left is horizontal shifting, so we need to shift the x-coordinate to left by 2 units as:

`(x+2)^2+y^2=25`

Since the translation by four units down refers to vertical shifting, so we will shift the y-coordinates of our given equation upwards by 4 units as:

`(x+2)^2+(y-4)^2=25`

Therefore, option D is the correct choice.