The line lx + my + n = 0 will touch the parab | vedclass

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(C) The given line is $lx + my + n = 0$,which can be rewritten as $y = -\frac{l}{m}x - \frac{n}{m}$.The condition for a line $y = mx + c$ to be tangen

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$ln = am^2$

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(C) The given line is $lx + my + n = 0$,which can be rewritten as $y = -\frac{l}{m}x - \frac{n}{m}$.The condition for a line $y = mx + c$ to be tangent to the parabola $y^2 = 4ax$ is $c = \frac{a}{m}$.Here,the slope of the line is $M = -\frac{l}{m}$ and the intercept is $C = -\frac{n}{m}$.Substituting these into the condition $C = \frac{a}{M}$,we get:$-\frac{n}{m} = \frac{a}{-l/m}$$-\frac{n}{m} = -\frac{am}{l}$$ln = am^2$.

The line $lx + my + n = 0$ will touch the parabola $y^2 = 4ax$,if

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