Open Question: Circle x^2 + y^2 -8x-4y=9?
Circle : x² + y² - 8x - 4y = 9
? ( x - 4 )² + ( y - 2 )² = 29
? C = ( 4, 2 ), r = v(29) ............. (1)
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Mid-Point of AB = ( (2+6)/2, (7-3)/2 ) = ( 4, 2 ) = C ..... (2)
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l (AB) = v[(6-2)²+(-3-7)² = v(16+100) = v(116) = 2v(29) = 2r ..... (3)
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From (1), (2), (3),
seg AB is a diameter. .................. Q.E.D.
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Happy To Help !
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