16. If x + xy + yº = 0 represents pair of lines then minimum value of a1 =​

Question

16.
If x + xy + yº = 0 represents pair of lines then minimum value of a1 =​

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Serenity 2 months 2021-08-11T12:51:29+00:00 1 Answer 0 views 0

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    0
    2021-08-11T12:53:28+00:00

    Step-by-step explanation:

    Let equation of the lines given by x

    2

    +2hxy+y

    2

    =0 be

    y=m

    1

    x and

    y=m

    2

    x.

    Since these lines make an angel a with y+x=0 whose slope is −1.

    1−m

    1

    m

    1

    +1

    =tana=

    1−m

    2

    −1−m

    2

    ⇒m

    1

    =

    tana+1

    tana−1

    and m

    2

    =

    tana−1

    tana+1

    ⇒m

    1

    +m

    2

    =

    tan

    2

    a−1

    (tana−1)

    2

    +(tana+1)

    2

    =

    cos2a

    2sec

    2

    a×cos

    2

    a

    =−2sec2a=−2h.

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