MCQ
The point $(4, -3)$ with respect to the ellipse $4{x^2} + 5{y^2} = 1$
- ALies on the curve
- BIs inside the curve
- ✓Is outside the curve
- DIs focus of the curve
$(i)$ On the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} - 1 = 0$ if
$\frac{{x_1^2}}{{{a^2}}} + \frac{{y_1^2}}{{{b^2}}} - 1 = 0$
$(ii)$ Outside the ellipse if $\frac{{x_1^2}}{{{a^2}}} + \frac{{y_1^2}}{{{b^2}}} - 1 > 0$
$(iii)$ Inside the ellipse if $\frac{{x_1^2}}{{{a^2}}} + \frac{{y_1^2}}{{{b^2}}} - 1 < 0$
Given ellipse is $\frac{{{x^2}}}{{1/4}} + \frac{{{y^2}}}{{1/5}} = 1$
$\frac{{16}}{{1/4}} + \frac{9}{{1/5}} - 1 = 64 + 45 - 1 > 0$
Point $(4, -3)$ lies outside the ellipse.
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$\mathrm{S}_{1} =\left\{\mathrm{z} \in \mathrm{C}|| \mathrm{z}-3-\left.2 \mathrm{i}\right|^{2}=8\right\}$
$\mathrm{S}_{2} =\{\mathrm{z} \in \mathrm{C} \mid \operatorname{Re}(\mathrm{z}) \geq 5\} \text { and }$
$\mathrm{S}_{3} =\{\mathrm{z} \in \mathrm{C} \| \mathrm{z}-\bar{z} \mid \geq 8\}$
Then the number of elements in $\mathrm{S}_{1} \cap \mathrm{S}_{2} \cap \mathrm{S}_{3}$ is equal to: