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Let a and b be non-zero real numbers. Then, the equation (ax2 + by2 + c) (x2 – 5xy + 6y2 ) = 0 represents (A) four straight lines, when c = 0 and a, b are of the same sign (B) two straight lines and a circle, when a = b, and c is of sign opposite to that of a (C) 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 (D) a circle and an ellipse, when a and b are of the same sign and c is of sign opposite to that of a

Let a and b be non-zero real numbers. Then, the equation (ax2 + by2 + c) (x2 – 5xy + 6y2 ) = 0 represents
(A) four straight lines, when c = 0 and a, b are of the same sign
(B) two straight lines and a circle, when a = b, and c is of sign opposite to that of a
(C) 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
(D) a circle and an ellipse, when a and b are of the same sign and c is of sign opposite to that of a 

Grade:11

1 Answers

grenade
2061 Points
6 years ago
(B)
(ax2 + by2 + c) (x2 – 5xy + 6y2 ) = 0 ⇒ ax2 + by2 + c = 0 or x2 – 5xy + 6y2 = 0 ⇒Hence the given equation represents two straight lines and a circle, when a = b and c is of sign opposite to that of a. 

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