The line y = mx + c is a normal to the ellips | vedclass

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(C) The equation of the line is $mx - y + c = 0$. Comparing this with $Lx + My + N = 0$,we have $L = m$,$M = -1$,and $N = c$. The condition for the li

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$\pm \frac{(a^2 - b^2)m}{\sqrt{a^2 + b^2m^2}}$

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(C) The equation of the line is $mx - y + c = 0$. Comparing this with $Lx + My + N = 0$,we have $L = m$,$M = -1$,and $N = c$. The condition for the line $Lx + My + N = 0$ to be a normal to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is given by $\frac{a^2}{L^2} + \frac{b^2}{M^2} = \frac{(a^2 - b^2)^2}{N^2}$. Substituting the values of $L, M, N$: $\frac{a^2}{m^2} + \frac{b^2}{(-1)^2} = \frac{(a^2 - b^2)^2}{c^2}$ $\frac{a^2 + b^2m^2}{m^2} = \frac{(a^2 - b^2)^2}{c^2}$ $c^2 = \frac{m^2(a^2 - b^2)^2}{a^2 + b^2m^2}$ $c = \pm \frac{(a^2 - b^2)m}{\sqrt{a^2 + b^2m^2}}$.

The line $y = mx + c$ is a normal to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$,if $c = $

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