JEE Main & Advanced Mathematics Conic Sections Question Bank Ellipse

  • question_answer
    The foci of the ellipse \[25{{(x+1)}^{2}}+9{{(y+2)}^{2}}=225\] are at [MNR 1991; MP PET 1998; UPSEAT 2000]

    A)            (?1, 2) and (?1, ?6)                   

    B)            (?1, 2) and (6, 1)

    C)            (1, ?2) and (1, ?6)                     

    D)            (?1, ?2) and (1, 6)

    Correct Answer: A

    Solution :

               \[\frac{{{(x+1)}^{2}}}{\frac{225}{25}}+\frac{{{(y+2)}^{2}}}{\frac{225}{9}}=1\]                    \[a=\sqrt{\frac{225}{25}}=\frac{15}{5},\,b=\sqrt{\frac{225}{9}}=\frac{15}{3}\] Þ \[e=\sqrt{1-\frac{9}{25}}=\frac{4}{5}\]                    Focus\[=\left( -1,-2\pm \frac{15}{3}.\frac{4}{5} \right)=(-1,-2\pm 4)\]=(?1,2); (?1,?6) .


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