Question

write an equation for the translation of (x-2)^2 + (y+1)^2 = 16 by four units left and 6 units up?

Answer 1

The equation of the circle has the form \(\Large (x-h)^2+(y-k)^2=r^2\) where h represents horizontal translation and k represents vertical translation. To translate \(\large (x-2)^2+(y+1)^2=16\) 4 units left and 6 units up, you need to subtract 4 from the h value and add 6 units to the k value.

Answer 2

okay, let me try.. hold on

Answer 3

what is r^2? 16^2 ?

Answer 4

igrnore that part. It's not important in this case

Answer 5

i got (x-6)^2 + (y+7)^2 but that isn't one of my choices

Answer 6

What are your answer choices?

Answer 7

(x+2)^2 + (y-5)^2, (x-2)^2 + (y-5)^2, (x+5)^2 + (y-2)^2, and (x+4)^2 + (y-5)^2

Answer 8

Hmm..odd. I don't know. @Michele_Laino

Answer 9

neither do i

Answer 10

such traslation is:
\[\Large \begin{gathered}
x \to x + 4 = X \hfill \\
y \to y + 6 = Y \hfill \\
\end{gathered} \]
where \(X,\;Y\) are the new variables

Answer 11

I don't understand what you mean

Answer 12

@michele_laino

Answer 13

please replace, into the original equation, \(x,y\) with \(X-4,Y-6\) respectively, what do you get?

Answer 14

for example, we can write this:
\(x-2--->X-4-2=X-6\)
and
\(y+1---> Y-6+1=Y-5\)

Answer 15

hint:
after that substitution, we get this equation:

\[\Large {\left( {X - 6} \right)^2} + {\left( {Y - 5} \right)^2} = 16\]
is it correct?

Answer 16

But wouldn't it be +6, not -6, since it is 6 unites up, not down

Answer 17

yes! And the new variable is \(Y=y+6\) where \(y\) is the old variable

Answer 18

1 + 6 = 7, so you'd get (y+7)^2, right? Except that not an answer choice