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JEE Main & Advanced Mathematics Conic Sections Question Bank Self Evaluation Test - Conic Sections

  • question_answer
    If a Point \[P(x,y)\] moves along the ellipse \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1\] and if C is the centre of the ellipse, then, 4 max \[\{CP\}+5min\{CP\}=\]

    A) 25

    B) 40

    C) 45

    D) 54

    Correct Answer: B

    Solution :

    [b] Given \[e{{q}^{n}}\] of ellipse is \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1\] \[\Rightarrow a=5\] and \[b=4\] Since \[p(x,\,\,y)\] moves along ellipse and C is the center \[\therefore \] max (CP) = 5 and min (CP) = 4 \[\therefore \] 4 Max \[\{cp\}+5min(cp)=4\times 5+5\times 4=40\]


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