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10-2. Parabola, Ellipse, Hyperbola
normal
The distance between the focii of the ellipse $(3x - 9)^2 + 9y^2 =(\sqrt 2 x + y +1)^2$ is-
A
$(3{ \sqrt 2 }-1)$
B
$\frac{{(3\sqrt 2 + 1) }}{{\sqrt 3 }}$
C
${(3\sqrt 2 + 1) }$
D
$\frac{{(3\sqrt 2 + 1) }}{{4\sqrt 3 }}$
Solution
$(x-3)^{2}+y^{2}=\frac{1}{3}\left(\frac{\sqrt{2} x+y+1}{\sqrt{3}}\right)^{2}$
focus $(3,0) $ and directrix is $\sqrt{2} x+y+c=0$
$\frac{\mathrm{a}}{\mathrm{e}}-\mathrm{ae}=\frac{(3 \sqrt{2}+1)}{\sqrt{3}}$
$\mathrm{e}=\frac{1}{\sqrt{3}}$
$ \Rightarrow 2 \mathrm{ae}=\frac{(3 \sqrt{2}+1)}{4 \sqrt{3}}$
Standard 11
Mathematics
