Geo4.51

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Find the value of k if the lines 2x+3y-4=0 and kx+4y-2=0 are conjugate with respect to x^{2}+y^{2}=4\,

The condition for the two lines to be conjugate is

r^{2}(l_{1}l_{2}+m_{1}m_{2})=n_{1}n_{2}\,

The values are r^{2}=4,l_{1}=2,l_{2}=k,m_{1}=3,m_{2}=4,n_{1}=-4,n_{2}=-2\,

HEnce

4(2\cdot k+3\cdot 4)=(-4)(-2)\,

2k+12=2\,

k=-5\,


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