If a and c are positive real numbers and the | vedclass

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Question

Radius $=3a$

Length of major axis $=4c$

Now, (radius)<(Half of the length of major axis)

$3a < 2c$

$9{a^2} < 4{c^2}$

$9ac - 9{

Vedclass · Accepted Answer

$9ac -9a^2 -2c^2 > 0$

Vedclass · Answer

Radius $=3a$ Length of major axis $=4c$ Now, (radius)<(Half of the length of major axis) $3a < 2c$ $9{a^2} < 4{c^2}$ $9ac - 9{a^2} > 9ac - 4{c^2}$ $9ac - 9{a^2} - 2{c^2} > 9ac - 6{c^2}\,\,\,\,\,\,\,\,......\left( i \right)$ Again $3a < 2c$ $ \Rightarrow 9ac < 6{c^2}$ $ \Rightarrow 9ac - 6{c^2} < 0\,\,\,\,\,\,\,\,\,\,.....\left( {ii} \right)$ From $(i)$ and $(ii)$, $9ac - 9{a^2} - 2{c^2} > 0$

If $a$ and $c$ are positive real numbers and the ellipse $\frac{{{x^2}}}{{4{c^2}}} + \frac{{{y^2}}}{{{c^2}}} = 1$ has four distinct points in common with the circle $x^2 + y^2 = 9a^2$ , then

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