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If the equation ax^2 + 2hxy + by^2 + 2gx...

If the equation `ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0` represents a pair of parallel lines, prove that
`a/h = h/b = g/f`

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
D
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Knowledge Check

  • If the equation ax^2+2hxy+by^2+2gx+2fy+c=0 represents a pair of parallel lines, then the distance between them is

    A
    `2sqrt((g^2-ac)/(h^2+a^2))`
    B
    `2sqrt((g^2+ac)/(h^2+a^2))`
    C
    `3sqrt(((g^2+ac)/(a(a+b)))`
    D
    `3sqrt(((g^2-ac)/(a(a+b)))`

  • The equation x^(2) + y^(2) + 2gx + 2fy + c = 0 represents a point-circle when -

    A
    `g^(2) + f^(2) = -c`
    B
    `g^(2) - f^(2) = -c`
    C
    `g^(2) + f^(2) = c`
    D
    `f^(2) - g^(2) = c`

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