JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
In a group of \(100\) persons \(75\) speak English and \(40\) speak Hindi. Each person speaks at least one of the two languages. If the number of persons, who speak only English is \(\alpha\) and the number of persons who speak only Hindi is \(\beta\), then the eccentricity of the ellipse \(25\left(\beta^2 x^2+\alpha^2 y^2\right)=\alpha^2 \beta^2\) is \(.......\)
- A \(\frac{3 \sqrt{15}}{12}\)
- B \(\frac{\sqrt{117}}{12}\)
- C \(\frac{\sqrt{119}}{12}\)
- D \(\frac{\sqrt{129}}{12}\)
Answer & Solution
Correct Answer
(C) \(\frac{\sqrt{119}}{12}\)
Step-by-step Solution
Detailed explanation
\(\alpha+ p =75\) \(\beta+ p =40\) \(\alpha+\beta+ p =100\) \(\text { From }(1),(2) \text { and (3) }\) \(P =15, \alpha=60 \text { and } \beta=25\) \(\text { Now equation of ellipse: } 25\left(\frac{ x ^2}{\alpha^2}+\frac{ y ^2}{\beta^2}\right)=1\)…
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