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10-2. Parabola, Ellipse, Hyperbola
medium
Find the equation for the ellipse that satisfies the given conditions: Ends of major axis $(±3,\,0)$ ends of minor axis $(0,\,±2)$
Option A
Option B
Option C
Option D
Solution
Ends of major axis $(±3,\,0)$ , ends of minor axis $(0,\,±2)$
Here, the major axis is along the $x-$ axis.
Therefore, the equation of the ellipse will be of the form $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1,$ where a is the semi major axis.
Accordingly, $a=3$ and $b=2$
Thus, the equation of the ellipse is $\frac{x^{2}}{3^{2}}+\frac{y^{2}}{2^{2}}=1$ or $\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$
Standard 11
Mathematics
