SOLUTION: plot x^2+4.y^2-4.x-8.y+4=0

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Question 44641: plot x^2+4.y^2-4.x-8.y+4=0
Answer by adamchapman(301) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B4.y%5E2-4.x-8.y%2B4=0
Rearrange to give a quadratic equation in terms of y:
4y%5E2-8y%2B%28x%5E2-4x%2B4%29=0
Now solve the quadratic using y+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29+,
where
a=4
b=-8
c=x%5E2-4x%2B4
This should give
y+=+%288+%2B-+sqrt%28+64-16%28x%5E2-4x%2B4%29%29%29%2F8+
x%5E2-4x%2B4 has two equal roots %28x-2%29%5E2=%28x%5E2-4x%2B4%29, so the quadratic solver for y becomes:
y+=+%288+%2B-+sqrt%28+64-16%28x-2%29%5E2%29%29%2F8+
y+=+1+%2B-+sqrt%28+64-16%28x-2%29%5E2%29%2F8+
There are two existing solutions for y:
y+=+1+%2B+sqrt%28+64-16%28x-2%29%5E2%29%2F8+ and y+=+1+-+sqrt%28+64-16%28x-2%29%5E2%29%2F8+.
I have plotted both of the lines below for you.
+graph%28+300%2C+200%2C+0%2C+4%2C+-10%2C+10%2C+1+%2B+sqrt%28+64-16%28x-2%29%5E2%29%2F8%2C+1+-+sqrt%28+64-16%28x-2%29%5E2%29%2F8%29+

I hope this helps.
P.S. I am trying to start up my own homework help website. I would be extremely grateful if you would e-mail me some feedback on the help you received to adam.chapman@student.manchester.ac.uk
Adam