- Home
- Standard 11
- Mathematics
10-2. Parabola, Ellipse, Hyperbola
medium
उस दीर्घवृत्त का समीकरण ज्ञात कीजिए, जिसके दीर्घ अक्ष की लंबाई $20$ है तथा नाभियाँ $(0,±5)$ हैं।
A
$\frac{x^{2}}{75}+\frac{y^{2}}{100}=1$
B
$\frac{x^{2}}{75}+\frac{y^{2}}{100}=1$
C
$\frac{x^{2}}{75}+\frac{y^{2}}{100}=1$
D
$\frac{x^{2}}{75}+\frac{y^{2}}{100}=1$
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
