MCQ
The equation of the ellipse whose centre is at origin and which passes through the points $(-3, 1)$ and $(2, -2)$ is
- A$5{x^2} + 3{y^2} = 32$
- ✓$3{x^2} + 5{y^2} = 32$
- C$5{x^2} - 3{y^2} = 32$
- D$3{x^2} + 5{y^2} + 32 = 0$
Since it passes through $(-3, 1)$ and $(2, -2)$,
so $\frac{9}{{{a^2}}} + \frac{1}{{{b^2}}} = 1$ and $\frac{1}{{{a^2}}} + \frac{1}{{{b^2}}} = \frac{1}{4}$
==>${a^2} = \frac{{32}}{3}$, ${b^2} = \frac{{32}}{5}$
Hence required equation of ellipse is $3{x^2} + 5{y^2} = 32$.
Trick : Since only equation $3{x^2} + 5{y^2} = 32$ passes through $(-3, 1)$ and $(2, -2)$. Hence the result.
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$\mathop {\lim }\limits_{x \to 0} \,\frac{{\tan \,(\pi \,{{\sin }^2}\,x) + \,{{(\left| x \right|\, - \,\sin \,(x\,[x]))}^2}}}{{{x^2}}}$