JEE MAIN - Mathematics Hindi (2025 - 8th April Evening Shift - No. 7)
Explanation
$$\begin{aligned} &E: \frac{x^2}{4 / 3}+\frac{y^2}{4 / P}=1\\ &\text { Centre of circle }(1,2) \text {, radius }\\ &\mathrm{r}=\sqrt{1+4+11} \end{aligned}$$
$$\mathrm{r}=4$$
$\because$ E pass from centre $(1,2)$
$$\therefore \frac{3}{4}+\mathrm{P}=1$$
$\mathrm{P}=\frac{1}{4} \quad \therefore$ vertical ellipse
$$\begin{aligned} & \mathrm{e}=\sqrt{1-\frac{4 / 3}{16}}=\sqrt{1-\frac{1}{12}}=\sqrt{\frac{11}{12}} \\ & \therefore \text { Focal distance of } \mathrm{C}(\mathrm{~h}, \mathrm{k}) \\ & =\mathrm{b} \pm \mathrm{ek} \\ & \mathrm{~F}_1=4+\sqrt{\frac{11}{12}} \times 2 \\ & \mathrm{~F}_2=4-\sqrt{\frac{11}{12}} \times 2 \\ & \therefore \mathrm{~F}_1 \mathrm{~F}_2=16-\frac{11}{3}=\frac{37}{3} \end{aligned}$$
$\therefore 6 \mathrm{~F}_1 \mathrm{~F}_2-\mathrm{r}=74-4=70$
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