If the sum of the slopes of the lines given by x^{2}-2cxy-7y^{2}=0  is four times their product, then c has the value

  • Option 1)

    2

  • Option 2)

    –1

  • Option 3)

         1

  • Option 4)

    –2

 

Answers (1)

As we learnt in

General equation of a conic -

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

- wherein

a,b,c, f,g,h  are constants

 

 x^{2}=2cxy-7y^{2}=0

Divide equation by

 x^{2};\frac{y}{x}=m\\ 1-2cm-7m^{2}=0\\ 7m^{2}+2cm-1=0\\ m_{1}+m_{2}=4m_{1}m_{2}

-\frac{2c}{7}=4\times \frac{-1}{7}\\ C=2


Option 1)

2

This option is correct 

Option 2)

–1

This option is incorrect 

Option 3)

     1

This option is incorrect 

Option 4)

–2

This option is incorrect 

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