Question

Write an equation for the translation of x^2+y^2=25 by 7 units left and 2 units down.
(x+7)^2+(y+2)^2=25
(x-7)^2+(y+2)^2=25
(x+7)^2+(y-2)^2=25
(x-7)^2+(y-2)^2=25

Answer 1

@TheSmartOne

Answer 2

@Luigi0210

Answer 3

Okayy, so we have the equation of \(\Large x^2+y^2=25\) correct? Do you know what the center of this equation is?

Answer 4

No I don't. Will you help me?

Answer 5

Actually is the center just (0,0)? Because that is the center of the equation.

Answer 6

In order to under it, you'll need to know the basics of the conic shapes.
And yes, the center would be (0,0) with a radius of 5.

Now, we want to move it 7 units to the left, and 2 units down, like so:

(pretend that circle is the center)

When we do that, we are moving in the x-direction (positively) and y-direction (negatively).. which in a coordinate point is (7, -3)
The radius won't change though

So change the (0, 0) to (7, -3) in \(\Large (x-0)^2+(y-0)^2=25 \)

Answer 7

*(7, -2) not (7, -3) my mistake

Answer 8

So C would be correct?

Answer 9

In short, \(\Large (\color{red}{7}, \color{blue}{-2}) \) will be the new \(\Large (\color{red}{h}, \color{blue}{k})\)

And nope, try again:
\(\Large (x-\color{red}{h})^2 +(y-\color{blue}{k}) =25 \)

\(\Large (x-\color{red}{7})^2 +(y-\color{blue}{(-2)}) =25 \)

Do understand it some at least?

Answer 10

Forgot the squares, but you get the point right?

Answer 11

So the opposite. -7 +2?

Answer 12

Yup! Gotta watch out for those negatives.

Answer 13

It'll end up looking like this:
http://prntscr.com/9o39l6