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    a) show that the line y=3x + 10 is a tangent to the circle x^2 + y^2 = 10

    b) draw a sketch showing the line and the circle above and hence write down the equation of another line 'passing through the point (0,10)' which is also a tangent to the circle x^2 + y^2 =10


    thank you so much for any help
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    cheers
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    (Original post by lolman42)
    a) show that the line y=3x + 10 is a tangent to the circle x^2 + y^2 = 10

    b) draw a sketch showing the line and the circle above and hence write down the equation of another line 'passing through the point (0,10)' which is also a tangent to the circle x^2 + y^2 =10


    thank you so much for any help
    Well, substitute the equation of the line into the circle and consider the nature of the resulting quadratic.

    Hint:

    It's a tangent if

    b^2 = 4ac
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    (Original post by Indeterminate)
    Well, substitute the equation of the line into the circle and consider the nature of the resulting quadratic.

    Hint:

    It's a tangent if

    b^2 = 4ac
    sorry I got part a) but for b)? thanks
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    (Original post by lolman42)
    sorry I got part a) but for b)? thanks
    Hint:

    The line can be horizontal, you know
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    (Original post by Indeterminate)
    Hint:

    The line can be horizontal, you know
    hmmm... still not to sure ..
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    (Original post by Indeterminate)
    Hint:

    The line can be horizontal, you know
    Not sure that helps
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    (Original post by TenOfThem)
    Not sure that helps
    do you mind explaining it, tenofthem? thanks .
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    (Original post by lolman42)
    hmmm... still not to sure ..
    Use symmetry

    I assume that you have found where the first line met the circle ... symmetry will tell you where this new line meets the circle

    Then you have 2 points, therefore an equation
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    (Original post by lolman42)
    hmmm... still not to sure ..
    (0, root 10) is at the top of the circle, right?

    So, which flat line touches the circle at this point?

    Think!!!

    If you can't get it, get back to me
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    (Original post by lolman42)
    do you mind explaining it, tenofthem? thanks .
    Takes time to type you know !
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    (Original post by Indeterminate)
    (0,10) is at the top of the circle, right?
    No, it isn't
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    (Original post by TenOfThem)
    Use symmetry

    I assume that you have found where the first line met the circle ... symmetry will tell you where this new line meets the circle

    Then you have 2 points, therefore an equation
    nope I haven't found where the first line meets the circle
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    (Original post by lolman42)
    nope I haven't found where the first line meets the circle
    well it is not much beyond the work you did for (a)
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    (Original post by TenOfThem)
    No, it isn't
    eek

    (0,\sqrt{10})
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    (Original post by TenOfThem)
    well it is not much beyond the work you did for (a)
    sub in when x =0 to find y?
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    (Original post by lolman42)
    sub in when x =0 to find y?
    no

    didn't you have a quadratic with a single solution as part of (a)
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    (Original post by TenOfThem)
    no

    didn't you have a quadratic with a single solution as part of (a)
    yeap..
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    (Original post by TenOfThem)
    no

    didn't you have a quadratic with a single solution as part of (a)
    subbing the equation of the line into the circle I get

    7x^2 + 60x + 90 = 0

    what do I do from here?
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    (Original post by lolman42)
    sub in when x =0 to find y?
    Surely, as it's saying "write down", it's asking for

    y=\sqrt{10}
 
 
 
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