Let \( a \) and \( b \) be nonzero real numbers. Then the equation ...
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Let \( a \) and \( b \) be nonzero real numbers. Then the equation
P \( \left(a x^{2}+b y^{2}+c\right)\left(x^{2}-5 x y+6 y^{2}\right)=0 \) represents
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(1) four straight lines, when \( c=0 \) and \( a, b \) are of the same sign
(2) two straight lines and a circle, when \( a=b \) and \( c \) is of sign opposite to that of \( a \)
(3) two straight lines and a hyperbola, when \( a \) and \( b \) are of the same sign and \( c \) is of sign opposite to that of \( a \)
(4) a circle and an ellipse, when \( a \) and \( b \) are of the same sign and \( c \) is of \( \operatorname{sign} \) opposite to that of \( a \)
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