What is an equation for the translation of x^2+y^2=10 by 3 units right and 2 units down?

Please show all steps!

Question

What is an equation for the translation of x^2+y^2=10 by 3 units right and 2 units down?

Please show all steps!

anonymous · Answer

@Mertsj

mertsj · Answer

Do you recognize what that equation would be if you graphed it?

anonymous · Answer

A smaller circle?

mertsj · Answer

It would be a circle.  What is its center?

anonymous · Answer

0,0 I believe

mertsj · Answer

Very good!!!  So if you moved that center 3 units to the right and 2 units down, what would its new center be?

anonymous · Answer

(3,-2)... I think?

mertsj · Answer

Yes.  You're on a roll.  Can you write that same equation with the new center?

anonymous · Answer

Ooh yay! I had no idea I could do this lol. And hang on, let me try.

anonymous · Answer

3^2+(-2)^2=10

mertsj · Answer

Close.  what happened to the x and y?

mertsj · Answer

$$(x-3)^2+(y+2)^2=10$$

mertsj · Answer

You have to have the x and y because they represent all the gazillions of points that make up the circle.

anonymous · Answer

Oh okay, that makes sense. But why are the signs switched in the new equation? If the points are 3 and -2, shouldn't the equation be x+3 and y-2 instead?

mertsj · Answer

Because the general equation of a circle with center (h,k) and radius r is:

mertsj · Answer

$$(x-h)^2+(y-k)^2=r^2$$

mertsj · Answer

So if you put 3 where the h is and -2 where the k is you will get the equation I posted above.

anonymous · Answer

Oh ookay. The second part got switched to a positive because it was already a negative

mertsj · Answer

Bingo!!

anonymous · Answer

Thanks so much for your help!!! :)

mertsj · Answer

yw