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P (2 , k) is on the ellipse x^(2) + 2y^(...

P (2 , k) is on the ellipse `x^(2) + 2y^(2) = 6 ` . For what value of k the point P is nearest to the line x + y = 7 ?

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Knowledge Check

  • Lines x + y = 1 and 3y = x + 3 intersect the ellipse x^(2) + 9y^(2) = 9 at the points P , Q , R . The area of the triangle PQR is _

    A
    `(36)/(5)`
    B
    `(18)/(5)`
    C
    `(9)/(5)`
    D
    `(1)/(5)`

  • Let the foci of the ellipse (x^(2))/(9) + y^(2) = 1 subtend a right angle at a point P . Then the locus of P is _

    A
    `x^(2) +y^(2) = 1 `
    B
    `x^(2) +y^(2) = 2 `
    C
    `x^(2) + y^(2) = 4 `
    D
    `x^(2)+ y^(2) = 8 `

  • Let P be a point on the ellipse (x^(2))/(16) + (y^(2))/(9) = 1 . If the distance of P from centre of the ellipse be equal with the average value of semi major axis and semi minor axis, then the coordinates of P is _

    A
    `((2sqrt(91))/(7),(3sqrt(105))/(14))`
    B
    `((2sqrt(91))/(7),(3sqrt(105))/(14))`
    C
    `(-(2sqrt(105))/(7),-(3sqrt(91))/(14))`
    D
    `(-(2sqrt(105))/(7),(3sqrt(91))/(14))`

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