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C1 circles help

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    I don't understand the very last part to these questions, 'Find the values of k for which the line is a tangent to the circle'.

    I've worked out that k = -3/4 and k = 4/3.. if i put these into the line equation I get Y = -3/4x + 6 and y = 4/3X + 6.. how do I know these lines are tangents to the circle?

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    (Original post by tom472)
    I don't understand the very last part to these questions, 'Find the values of k for which the line is a tangent to the circle'.

    I've worked out that k = -3/4 and k = 4/3.. if i put these into the line equation I get Y = -3/4x + 6 and y = 4/3X + 6.. how do I know these lines are tangents to the circle?

    Click image for larger version. 

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ID:	147020
    You've found the equation for where they intersect. And then you've found an equation in k when these have 1 repeated root. Do you remember what one repeated root means?


    Say if I gave you a regular quadratic with 1 repeated root (b^2 - 4ac = 0) how would you describe what that graph looks like?
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    If it had one repeated root does that mean it touches the x axis once? Sorry I still don't get how I know theyre tangents
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    (Original post by tom472)
    If it had one repeated root does that mean it touches the x axis once? Sorry I still don't get how I know theyre tangents
    Yep that's right. So if we've made this straight line and this circle equal (by subbing in for y like you did) and they only have one repeated root then the same thing applies; the line only 'touches' the circle i.e. it's a tangent.
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    (Original post by hassi94)
    Yep that's right. So if we've made this straight line and this circle equal (by subbing in for y like you did) and they only have one repeated root then the same thing applies; the line only 'touches' the circle i.e. it's a tangent.
    How do you do 7)d)i?
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    (Original post by GreenLantern1)
    How do you do 7)d)i?
    sub y = kx + 6 into the equation of the circle, expand and simplify.
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    (Original post by hassi94)
    sub y = kx + 6 into the equation of the circle, expand and simplify.
    Ahh I see know, cheers

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