The line lx + my + n = 0 is a normal to the ellipse \(\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1\) if
1
\(\frac{{{a^2}}}{{{l^2}}} - \frac{{{b^2}}}{{{m^2}}} = \frac{{{{\left( {{a^2} - {b^2}} \right)}^2}}}{{{n^2}}}\)
2
\(- \frac{{{a^2}}}{{{l^2}}} - \frac{{{b^2}}}{{{m^2}}} - \frac{{{{\left( {{a^2} - {b^2}} \right)}^2}}}{{{n^2}}} = 0\)
3
\(\frac{{{a^2}}}{{{l^2}}} + \frac{{{b^2}}}{{{m^2}}} = \frac{{{{\left( {{a^2} - {b^2}} \right)}^2}}}{{{n^2}}}\)
4
\(\frac{{{a^2}}}{{{l^2}}} + \frac{{{b^2}}}{{{m^2}}} + \frac{{{{\left( {{a^2} - {b^2}} \right)}^2}}}{{{n^2}}} = 0\)