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A(2, 3), B(-1, 1) are two points if P is...

`A(2, 3), B(-1, 1)` are two points if P is a point such that `angleAPB=90^(@)` then the locus of P is

A

`x^(2)+y^(2)-x-4y+1=0`

B

`x^(2)+y^(2)+x+4y-1=0`

C

`x^(2)+y^(2)-x+4y-1=0`

D

`x^(2)+y^(2)+x-4y-1=0`

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Knowledge Check

  • A ( 2, 3 ) , B ( - 1, 1 ) are two points . If P is a point such that angle APB = 90 ^@ , then the locus of P is

    A
    ` x ^2 + y ^ 2 - x - 4y + 1 = 0 `
    B
    ` x ^ 2 + y ^ 2 + x + 4y - 1 = 0 `
    C
    ` x ^ 2 + y ^ 2 - x + 4 y - 1 = 0 `
    D
    ` x ^ 2 + y ^ 2 + x - 4 y + 1 = 0 `

  • A(2, 1) and B(1, 2) are two points. If P is a point such that PA : PB = 2:1 , then the locus of P is

    A
    `3x^(2)+3y^(2)+4x+14y-15=0`
    B
    `3x^(2)+3y^(2)-4x-14y+15=0`
    C
    `3x^(2)+3y^(2)+2x+7y+13=0`
    D
    `3x^(2)+3y^(2)-2x-7y+13=0`

  • I : If the distances from P to the points ( 3,4), ( - 3, 4) are in the ratio 3 : 2 , then the locus of P is 5 x ^ 2 + 5y ^ 2 + 78 x - 40 y + 125 = 0 II : A ( -9, 0) , B( -1, 0) are two points. If P is a point such that P A : PB = 3 : 1 , then the locus of P is x ^ 2 + y^ 2 = 9

    A
    only I is true
    B
    only II is true
    C
    both I and II are true
    D
    neither I nor II are true

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