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If the line l x+m y+n=0 touches the para...

If the line `l x+m y+n=0` touches the parabola `y^2=4a x ,` prove that `ln=a m^2`

Text Solution

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True
Given equation of a line is
lx+my+n=0
and parabola`y^(2)`=4ax
From Eq. (i), x=`-((my+n)/l)`put in Eq. (ii) we get
`y^(2)=-(4a(my+n))/l`
`rArr ly^(2)=-4amy-4ax`
`rArrly^(2)+3amy+4an=0`
For tangent, D=0
`rArr16a^(2)m^(2)=4lxx4an`
`rArr 16a^(2)m^(2)=16anl`
`rArr am^(2)=nl`
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