1. ## Help with Circles please

The question states:
Maraiah is making a graphic design on a computer using a coordinate grid. She began with a circle that has a center (0,0). Then, she drew a congruent cirlce with the equation x^2+y^2+12x+4y+5=0.

B)what translation did Maraiah make to draw the second circle?

What i did was, since the second equation is congruent to the fist one, i replaced the x and y with 0. However, the final statement results to be false. 5=0. And using (x-h)^2+(y-k)^2=r^2, i figured the radius to be 0.... i have no clue on how to this problem. Please guide me! Thanks guys.

2. Hello, jjkins!

Maraiah is making a graphic design on a computer using a coordinate grid.
She began with a circle that has a center (0,0).
Then, she drew a congruent cirlce with the equation $x^2+y^2+12x+4y+5\:=\:0$

Complete the square . . .

We have: . $(x^2 + 12x \qquad) + (y^2 + 4y \qquad) \;=\;-5$

. . . . . . . . $(x^2 + 12x + {\color{blue}36}) + (y^2 + 4y + {\color{red}4}) \;=\;-5 + {\color{blue}36} + {\color{red}4}$

. . . . . . . . . . . $(x+6)^2\quad+\quad(y+2)^2\quad \;= \quad\;35$

Radius of both circles: . $\sqrt{35}$

B) What translation did Maraiah make to draw the second circle?
The center of the second circle is: . $(\text{-}6,\,\text{-}2)$

She moved the original circle: 6 units to the left and 2 units down.