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The locus of the vertex of the family of...

The locus of the vertex of the family of parabolas `y=(a^3x^2)/3+(a^(2x))/2-2a` is `x y=(105)/(64)` (b) `x y=3/4` `x y=(35)/(16)` (d) `x y=(64)/(105)`

A

`xy=105/64`

B

`xy=3//4`

C

`xy=35/16`

D

`xy=64/105`

Text Solution

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The correct Answer is:
A
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The locus of the vertex of the family of parabolas y=(a^(3)x^(2))/(3)+(a^(2x))/(2)-2a is xy=(105)/(64) (b) xy=(3)/(4)xy=(35)/(16) (d) xy=(64)/(105)

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Knowledge Check

  • The locus of the vertices of the family of parabolas y=(a^3x^2)/3+(a^2x)/2-2a is

    A
    `xy=3/4`
    B
    `xy=(35)/(16)`
    C
    `xy=(64)/(105)`
    D
    `xy=(105)/(64)`

  • The vertex of the parabola y ^(2) -4y-x+3=0 is

    A
    `(-1, 3)`
    B
    `(-1, 2)`
    C
    `(2, -1)`
    D
    `(3,-1)`

  • Find the locus of the Orthocentre of the triangle formed by three tangents of the parabola (4x-3)^(2)=-64(2y+1)

    A
    `y=(-5)/2`
    B
    `y=1`
    C
    `x=7/4`
    D
    `y=3/2`

    • Similar Questions

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