SOLUTION: Find the equation of the ellipse (𝑥+1)^2/4+(y−1)^2/1=1 reflected in the line 𝑦=−x+1/2 . Also sketch it.

Algebra ->  College  -> Linear Algebra -> SOLUTION: Find the equation of the ellipse (𝑥+1)^2/4+(y−1)^2/1=1 reflected in the line 𝑦=−x+1/2 . Also sketch it.      Log On


   

Question 1157602: Find the equation of the ellipse (𝑥+1)^2/4+(y−1)^2/1=1 reflected in the line 𝑦=−x+1/2 . Also sketch it.
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!

The point (x,y) reflected in the line Ax+By+C=0 is the point



Since your line is 
y=-x%2B1%2F2
or
x%2By-1%2F2=0

A=1, B=1, C=-1/2



that simplifies to 

%28matrix%281%2C3%2C%0D%0A%0D%0A%28-2y%2B1%29%2F2%2C%22%2C%22%2C%28-2x%2B1%29%2F2%29%29

So in the ellipse equation, replace x by
%28-2y%2B1%29%2F2
and replace y by
%28-2x%2B1%29%2F2

and you'll get an equation of another ellipse.

I won't do that work for you, but here is the graph. The red
ellipse is the given one. The green one is the one reflected
in the line:

 

Edwin