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What is the sum of the major and minor axes of the ellipse whose eccentricity is $4 / 5$ and length of latus rectum is $14.4$ unit
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The correct answer is:
64 units
Let $2 \mathrm{a}$ and $2 \mathrm{~b}$ be the length of major and minor axis respectively.
$\frac{\mathrm{b}^{2}}{\mathrm{a}^{2}}=\frac{9}{25}$
Also, $\frac{2 \mathrm{~b}^{2}}{\mathrm{a}}=14.4$
$\frac{\mathrm{b}^{2}}{\mathrm{a}}=7.2, \mathrm{~b}^{2}=7.2 \mathrm{a}$
Putting value of $\frac{\mathrm{b}^{2}}{\mathrm{a}}$ in equation (i)
$\frac{7.2}{\mathrm{a}}=\frac{9}{25} \Rightarrow \mathrm{a}=20$
$b^{2}=7.2 \times 20=144$
$b=12$
the sum of the major and minor axes $=2 a+2 b$
$=2(\mathrm{a}+\mathrm{b})=2(20+12)=64$ units
$\frac{\mathrm{b}^{2}}{\mathrm{a}^{2}}=\frac{9}{25}$
Also, $\frac{2 \mathrm{~b}^{2}}{\mathrm{a}}=14.4$
$\frac{\mathrm{b}^{2}}{\mathrm{a}}=7.2, \mathrm{~b}^{2}=7.2 \mathrm{a}$
Putting value of $\frac{\mathrm{b}^{2}}{\mathrm{a}}$ in equation (i)
$\frac{7.2}{\mathrm{a}}=\frac{9}{25} \Rightarrow \mathrm{a}=20$
$b^{2}=7.2 \times 20=144$
$b=12$
the sum of the major and minor axes $=2 a+2 b$
$=2(\mathrm{a}+\mathrm{b})=2(20+12)=64$ units
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