2. Sample Papers
  3. JEE Main & Advanced

JEE Main & Advanced Sample Paper JEE Main Sample Paper-17

  • question_answer
    The value of a for the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1(a>b),\]if the extremities of the latus-rectum of the ellipse having positive ordinate lies on the parabola \[{{x}^{2}}=-2(y-2),\]is

    A)  3                                            

    B)  4

    C)  1/2                       

    D)  2

    Correct Answer: D

    Solution :

     \[\left( \pm \,ae,\frac{{{b}^{2}}}{a} \right)\]are extremities of the latus-rectum having positive ordinates which lies on parabola\[{{x}^{2}}=-2(y-2).\] \[\Rightarrow \]               \[{{a}^{2}}{{e}^{2}}=-2\left( \frac{{{b}^{2}}}{a}-2 \right)\]                             ?(i) Also \[{{b}^{2}}={{a}^{2}}(1-{{e}^{2}})\] From (i) and (i), we get \[{{a}^{2}}{{e}^{2}}-2a{{e}^{2}}+2a-4=0\] \[\Rightarrow \]\[a{{e}^{2}}(a-2)+2(a-2)=0\] \[\therefore \]\[(a{{e}^{2}}+2)(a-2)=0\] Hence, \[a=2.\]


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