if the line lx+my+n=0 is a normal to the ellipse x^{2 }/a^2+y^2/b^2=1, then find the conditio

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l x + m y + n = 0

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

\frac{a^{2}}{l^{2}} + \frac{b^{2}}{m^{2}}

l x + m y + n = 0

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

\frac{a^{2}}{l^{2}} + \frac{b^{2}}{m^{2}} = \frac{(a^{2} - b^{2})^{2}}{n^{2}}

l x + m y = n

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

\frac{n^{2}}{(a^{2} - b^{2})^{2}} (\frac{a^{2}}{l^{2}} + \frac{b^{2}}{m^{2}}) = k,

7 k =

l x + m y + n = 0

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

l x + m y + n = 0

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

\frac{a^{2}}{l^{2}} - \frac{b^{2}}{m^{2}} = {(\frac{a^{2} + b^{2}}{n})}^{2}

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