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Consider the equation of a circle x^2-2x+y^2-4y-4=0. If the line 2x-y+a=0 is its diameter. Then find the value of a.

2 answers

The circle is (x-1)^2 + (y-2)^2 = 9
so its center is at (1,2)
So you need 2*1-2+a = 0
a=0

see the graphs at

www.wolframalpha.com/input/?i=plot+x%5E2-2x%2By%5E2-4y-4%3D0%2C+2x-y+%3D+0
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