Find a positive value of α if the coordinat...
Find a positive value of α if the coordinate of the centre of a circle x2 + y2 - 2αx + 4y - α = 0 is (α, -2) and the radius is 4 units.
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Correct answer is C
x2+y2−2αx+4y−α=0
r = 4 units; centre (α, -2).
(x−x1)2+(y−y1)2=r2
(x−α)2+(y−(−2))2=42
x2−2αx+α2+y2+4y+4=16
α(α−3)+4(α−3)=0
(α+4)(α−3)=0⟹+α=3
x2+y2−2αx+4y=16−α2−4
∴
\alpha^{2} - 3\alpha + 4\alpha - 12 = 0
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