2. Solved Papers
  3. JEE Main & Advanced

JEE Main & Advanced JEE Main Paper (Held on 08-4-2019 Afternoon)

  • question_answer
    In an ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis is 10 and one of the foci is at \[\left( 0,5\sqrt{3} \right),\] then the length of its latus rectum is: [JEE Main 8-4-2019 Afternoon]

    A) 10                               

    B) 8

    C) 5         

    D) 6

    Correct Answer: C

    Solution :

                Let equation of ellipse\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] \[2a2b=10\]                                        ...(1) \[ae=5\sqrt{3}\]                                              ...(b2 \[\frac{2{{b}^{2}}}{a}=?\] \[{{b}^{2}}={{a}^{2}}(1-{{e}^{2}})\] \[{{b}^{2}}={{a}^{2}}-{{a}^{2}}{{e}^{2}}\] \[{{b}^{2}}={{a}^{2}}-25\times 3\] \[\Rightarrow \]\[b=5\]and \[a=10\] \[\therefore \] length of L.R.\[=\frac{2(25)}{10}=5\]


You need to login to perform this action.
You will be redirected in 3 sec spinner