Question 52222
<pre><font size = 6><b>
Find the equation you get when you move 
the unit circle up 3 units and left 5 
units

Rules:
1. To move any graph RIGHT h units, we 
replace x by (x - h) in its equation.

2. To move any graph LEFT h units, we 
replace x by (x + h) in its equation. 

3. To move any graph UP k units we, 
replace y by (y - k) in its equation.

4. To move any graph DOWN k units, we 
replace y by (y + k) in its equation.


The unit circle has equation

 x² + y² = 1

and its graph looks like this:

{{{ graph( 300, 300, -6, 6, -6, 6, sqrt(1-x^2), -sqrt(1-x^2)) }}}

So to move its graph up 3 units, 
we replace y by (y - 3) in that 
equation and get this new equation:

 x² + (y - 3)² = 1

which has this graph 

{{{ graph( 300, 300, -6, 6, -6, 6, sqrt(1-x^2)+3, -sqrt(1-x^2)+3) }}} 

Then to further move it 5 units left, 
we replace x by (x + 5) in that 
equation and get this new equation:

(x + 5)² + (y - 3)² = 1

which has this graph:

{{{ graph( 300, 300, -6, 6, -6, 6, sqrt(1-(x+5)^2)+3, -sqrt(1-(x+5)^2)+3) }}}

Edwin</pre>