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  • Let a and b be non–zero real numbers. Then, the equation <img alt="\mathrm{\left(a x^2+b y^2+(C)\left(x^2-5 x y+6 y^2\right)=0\right.}" src="https://entrancecorner.oncodecogs.com/gif.lat

Let a and b be non–zero real numbers. Then, the equation \mathrm{\left(a x^2+b y^2+(C)\left(x^2-5 x y+6 y^2\right)=0\right.} represent

 

Option: 1

 four straight lines, when c = 0 and a, b are of the same sign 

 

 


Option: 2

 two straight lines and a circle, when a = b, and c is of sign opposite to that of a 


Option: 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 

 


Option: 4

a circle and an ellipse, when a and b are of the same sign and c is of sign opposite to that o


Answers (1)

best_answer

\mathrm{x^2-5 x y+6 y^2=0}  represent a pair of lines passing through origin 

\mathrm{\begin{aligned} & a x^2+a y^2=-c \\ & \Rightarrow x^2+y^2=\frac{-c}{a}>0 \\ & \Rightarrow a x^2+a y^2+c=0 \text { represent \; a \; circle } \end{aligned}}

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