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10-2. Parabola, Ellipse, Hyperbola
easy
The line $lx + my - n = 0$ will be tangent to the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$, if
A
${a^2}{l^2} + {b^2}{m^2} = {n^2}$
B
$a{l^2} + b{m^2} = {n^2}$
C
${a^2}l + {b^2}m = n$
D
None of these
Solution
(a) $y = \frac{{ – l}}{m}x + \frac{n}{m}$ is tangent to $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$, if
$\frac{n}{m} = \pm \sqrt {{b^2} + {a^2}{{\left( {\frac{l}{m}} \right)}^2}} $ or ${n^2} = {m^2}{b^2} + {l^2}{a^2}$.
Standard 11
Mathematics
