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Let {a}{a}{n}{d}{b} be nonzero real numbers. Then the equation

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

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Let

a a n d b

be nonzero real numbers. Then the equation

(a x^{2} + b y^{2} + c) (x^{2} - 5 x y + 6 y^{2}) = 0

represents. four straight lines, when

c = 0

and

a, b

are of the same sign. two straight lines and a circle, when

a = b

and

c

is of sign opposite to that

a

two straight lines and a hyperbola, when

a a n d b

are of the same sign and

c

is of sign opposite to that of

a

a circle and an ellipse, when

a a n d b

are of the same sign and

c

is of sign opposite to that of

a

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Question Text

Let

a a n d b

be nonzero real numbers. Then the equation

(a x^{2} + b y^{2} + c) (x^{2} - 5 x y + 6 y^{2}) = 0

represents. four straight lines, when

c = 0

and

a, b

are of the same sign. two straight lines and a circle, when

a = b

and

c

is of sign opposite to that

a

two straight lines and a hyperbola, when

a a n d b

are of the same sign and

c

is of sign opposite to that of

a

a circle and an ellipse, when

a a n d b

are of the same sign and

c

is of sign opposite to that of

a

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