If the line lx + my + n = 0 is tangent to the | vedclass

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(C) The equation of the parabola is $y^{2} = 4ax$. Let the line $lx + my + n = 0$ be tangent to the parabola. Rewriting the line equation as $y = -\fr

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$ln = am^{2}$

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(C) The equation of the parabola is $y^{2} = 4ax$. Let the line $lx + my + n = 0$ be tangent to the parabola. Rewriting the line equation as $y = -\frac{l}{m}x - \frac{n}{m}$,which is in the form $y = mx + c$ where the slope $M = -\frac{l}{m}$ and intercept $C = -\frac{n}{m}$. The condition for the line $y = Mx + C$ to be tangent to the parabola $y^{2} = 4ax$ is $C = \frac{a}{M}$. Substituting the values of $M$ and $C$: $-\frac{n}{m} = \frac{a}{-l/m} = -\frac{am}{l}$. Multiplying both sides by $-1$,we get $\frac{n}{m} = \frac{am}{l}$. Cross-multiplying gives $nl = am^{2}$.

If the line $lx + my + n = 0$ is tangent to the parabola $y^{2} = 4ax$,then

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