SOLUTION: In how many points do the graphs of 2(x+1)^2 + (y-2)^2 = 25 and 4(x+1)^2 +3(y-2)^2= 15 intersect

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Question 1097494: In how many points do the graphs of 2(x+1)^2 + (y-2)^2 = 25 and 4(x+1)^2 +3(y-2)^2= 15 intersect
Answer by greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!


2%28x%2B1%29%5E2+%2B+%28y-2%29%5E2+=+25 (1)
4%28x%2B1%29%5E2+%2B3%28y-2%29%5E2=+15 (2)

Double equation (1)...

4%28x%2B1%29%5E2+%2B+2%28y-2%29%5E2+=+50 (3)

And subtract (3) from (2):

%28y-2%29%5E2+=+-35

This equation has no solution in real numbers; the graphs of the two ellipses will have no points of intersection.

The two graphs are ellipses with the same center, (-1,2). The major and minor axes of the first ellipse are both longer than the major and minor axes of the second; so the graph of the second ellipse will be completely inside the graph of the first, which of course means no points of intersection.