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If the pair of lines ax^2 +2hxy+ by^2+ 2...

If the pair of lines `ax^2 +2hxy+ by^2+ 2gx+ 2fy +c=0` intersect on the y-axis then

A

`2fgh = bg^(2)+ch^(2)`

B

`bg^(2)ne ch^(2)`

C

`abc=2fgh`

D

none of these

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • The principal axes of the hyperbola ax^(2) + 2hxy + by^(2) + 2gx + 2fy + c = 0 are parallel to the lines

    A
    `ax^(2) + 2hxy + by^(2) = 0 `
    B
    `h(x^(2) - y^(2)) = (a - b) xy `
    C
    `bx^(2) - 2hxy + ay^(2) = 0 `
    D
    `(a + b)(x^(2) - y^(2)) = h (a - b) xy `

  • If the coinc ax^(2) + 2hxy + by^(2) + 2gx + 2fy + c = 0 be a hyperbola , and the equation of the conjugate hyperbola is ax^(2) + 2hxy + by^(2) + 2gx + lambda = 0 , then lambda is equal to

    A
    `Delta/(ab - h^(2))`
    B
    `c + Delta/(ab - h^(2))`
    C
    `c - (2 Delta)/(ab - h^(2))`
    D
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    A
    `Delta =0,h^(2) lt ab`
    B
    `Delta ne 0, h^(2) lt ab`
    C
    `Delta ne 0, h^(2) gt ab`
    D
    `Delta ne 0, h^(2) = ab`

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