The equation \( \left(1+a^{2}\right) x^{2}+2 a^{2} x+a^{2}+b^{2}-1=0 \) has roots of opposite si...

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The equation \( \left(1+a^{2}\right) x^{2}+2 a^{2} x+a^{2}+b^{2}-1=0 \) has roots of opposite sign if \( (a, b) \) lies
(a) On a straight line \( x+y=1 \)
(b) Inside a circle of centre \( (0,0) \) and radius 1
(c) On a parabola of vertex \( (0,0) \) and focal length 1
(d) On a straight line \( x-y=1 \)
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