The line lx + my + n = 0 will be a tangent to | vedclass

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(B) The condition for the line $y = Mx + C$ to be a tangent to the circle $x^2 + y^2 = a^2$ is $C^2 = a^2(1 + M^2)$.Given the line $lx + my + n = 0$,w

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$a^2(l^2 + m^2) = n^2$

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(B) The condition for the line $y = Mx + C$ to be a tangent to the circle $x^2 + y^2 = a^2$ is $C^2 = a^2(1 + M^2)$.Given the line $lx + my + n = 0$,we can rewrite it as $y = -\frac{l}{m}x - \frac{n}{m}$.Here,the slope $M = -\frac{l}{m}$ and the intercept $C = -\frac{n}{m}$.Substituting these into the condition $C^2 = a^2(1 + M^2)$,we get:$(-\frac{n}{m})^2 = a^2(1 + (-\frac{l}{m})^2)$$\frac{n^2}{m^2} = a^2(1 + \frac{l^2}{m^2})$$\frac{n^2}{m^2} = a^2(\frac{m^2 + l^2}{m^2})$$n^2 = a^2(l^2 + m^2)$.

The line $lx + my + n = 0$ will be a tangent to the circle $x^2 + y^2 = a^2$ if

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