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A(1,2),B(2,- 3),C(-2,3) are 3 points. A ...

`A(1,2),B(2,- 3),C(-2,3)` are 3 points. A point P moves such that `PA^(2)+PB^(2)=2PC^(2)` . Show that the equation to the locus of P is 7 x - 7y + 4 = 0 .

Answer

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A(1,2),B(2,-3),C(-2,3) are 3 points A point P moves such that PA^(2)+PB^(2)=2PC^(2) . Show that the equation to the equation to the locus of 7x-7y+4=0 ,

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Knowledge Check

  • A (1, 2 ) , B (2, - 3 ), C ( - 2, 3 ) are three points. If P is a point moves such that PA^ 2 + PB^ 2 = 2 PC^ 2 , then the locus of P is

    A
    ` 7x - 7y + 4 = 0 `
    B
    ` 7 x + 7y - 4 = 0 `
    C
    ` 7 x + 7y + 4 = 0 `
    D
    ` 7 x - 7y - 4 = 0 `

  • Let A(1,0), B(-1,0), C(2, 0) then the locus of a point P such that PB^(2)+ PC^(2) = 2PA^(2) is

    A
    a straight line parallel to x - axis
    B
    a straight line parallel to y-axis
    C
    parallel to x + y =2
    D
    xy=0

  • A ( 2, 3 ) , B ( 1, 5 ) , C ( - 1, 2 ) are the three points. If P is a point moves such that P A^ 2 + PB^ 2 = 2 PC^ 2 , then the locus of P is

    A
    ` 10 x -8y + 29 = 0 `
    B
    ` 10 x + 8y - 29 = 0 `
    C
    `10 x + 8y + 29 = 0 `
    D
    ` 10 x - 8y - 29 = 0 `

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