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A point P moves such that sum of the slo...

A point P moves such that sum of the slopes of the normals drawn from it to the hyperbola xy=16 is equal to the sum of ordinates of feet of normals. The locus of P is a curve C

A

`x^(2)=4y`

B

`x^(2)=16y`

C

`x^(2)=12y`

D

`y^(2)=8x`

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • A point P moves such that the sum of the slopes of the normals drawn from it to the hyperbola xy = 16 is equal to the sum of ordinates of feet of normals . The locus of P is a curve C. If the tangent to the curve C cuts the corrdinate axes at A and B, then the locus of the middle point of AB is

    A
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    B
    `x^(2)=2y`
    C
    `x^(2)+2y=0`
    D
    `x^(2)+4y=0`

  • A point P moves such that the sum of the slopes of the normals drawn from it to the hyperbola xy = 16 is equal to the sum of ordinates of feet of normals . The locus of P is a curve C. The area of the equilateral triangle inscribed in the curve C having one vertex as the vertex of curve C is

    A
    `772 sqrt3"sq. units"`
    B
    `776sqrt3"sq. units"`
    C
    `760sqrt3"sq. units"`
    D
    `768sqrt3"sq. units"`

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    A
    `x^(2)+2y=0`
    B
    `x^(2)=y`
    C
    `2x^(2)+y=0`
    D
    `x^(2)=2y`

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