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  • The value of P for which the equation x^2+pxy+y^2-5x-7y =0 represent pair of straight line .

The value of P for which the equation x^2+pxy+y^2-5x-7y =0 represent pair of straight line .

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Solution: Given ,

                 x^2+pxy+y^2-5x-7y=0     ........(1)

        We know ,   ax^2+2hxy+by^2+2gx+2fy+c=0

        Represent a pair of straight line if 

                    Delta =abc+2fgh-af^2-bg^2-ch^2=0

       Now ,     a=1,h=fracp2,b=1,g=-frac52,f=-frac72  ,  c=0

        Hence ,     1 imes1 imes 0+2(-frac72)(-frac-52)(fracp2)-1(-frac72)^2-1(-frac52)^2=0

        Rightarrow              frac35p4=frac744Rightarrow p=frac7435.  

 

              

Posted by

Deependra Verma

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