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?

D.

Step-by-step explanation:

We have been given an equation . 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:

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:

Therefore, option D is the correct choice.

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.