Question 10203: Find the points of intersection of the graphs.
x^2 - y^2 - 2x + 2y = 0
4x^2 + y^2 - 8x = 0
Please and thank you
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! 
In fact, the 1st equation is two-lines and the 2nd one is an ellipse
Since  --> 
-->  is an ellipse centered at (1,0).
They may have at most 4 points of intersectins.
[The point is to cancel variable y]
Using complete squares to covert the 1st equation to:
 ...(1)
Keep the 2nd equation as before ...(2)
From(1),we have y-1 =  ( +/-means postive or negative)
When y = x-1 + 1 = x, goto (2), we have
 ,hence x = 0 or 8/5 (why??)
Then,we get y = 0 or 8/5 (since y = x)
When y = -x+1 + 1 = -x+2, goto (2), we have
 ,
Or  ,
Factoring: 
So,x = 2/5 or 2
and then, y = 8/5 or 0.
Thus,the four points of intersection are
(0,0),(8/5,8/5), (2/5, 8/5), and (2,0)
The graphs as:
Kenny
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