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The equation

x2y2- 2xy2- 3y2- 4x2y + 8xy + 12y = 0  represents

Option: 1

a pair of straight lines                                                   

                    


Option: 2

a pair of straight lines and a circle


Option: 3

a pair of straight lines and a parabola                            

 


Option: 4

a set of four lines forming a square


Answers (1)

best_answer

As we learned

condition for pair of straigth lines -

\Delta = 0


 

- wherein

\triangleright = abc+2fgh-af^{2}-bg^{2}-ch^{2}

For conic:

ax^{2}+by^{2}+2hxy+2gx+2fy+c=0

 

 

x2y2- 2xy2- 3y2- 4x2y + 8xy + 12y   = y2(x2-2x-3) - 4y(x2- 2x-3) = 0

 \Rightarrow y(y-4)(x- 3) (x + 1) = 0                 \Rightarrow y = 0, y = 4, x = 3, x = -1

       Hence the equation represents four straight lines which evidently form a square.

                        Hence correct answer is (d).

 

Posted by

avinash.dongre

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