Equation of ellipse, whose length of major axis is 20 and foci are (0,,pm 5)

Hindi

10-2. Parabola, Ellipse, Hyperbola

medium

Find the equation of the ellipse, whose length of the major axis is $20$ and foci are $(0,\,\pm 5)$

$\frac{x^{2}}{75}+\frac{y^{2}}{100}=1$

Solution

since the foci are on $y-$ axis, the major axis is along the $y-$ axis. So, equation of the cllipse is of the form $\frac{x^{2}}{b^{2}}+\frac{y^{2}}{a^{2}}=1$

Given that

$a=$ semi-major axis $=\frac{20}{2}=10$

and the relation $c^{2}=a^{2}-b^{2}$ gives

$5^{2}=10^{2}-b^{2} $ i.e., $b^{2}=75$

Therefore, the equation of the ellipse is

$\frac{x^{2}}{75}+\frac{y^{2}}{100}=1$

Standard 11

Mathematics

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