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    Alice22's Avatar
    Alice22 Posts: 3, Reputation: 1
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    #1

    Feb 7, 2010, 09:26 AM
    coordinate geometry equations
    Find the quadratic equation in x for the intersections of the line y=2x+c and the circle x^2 + y^2=20. Use the discriminant of the equation to determine the values of x which will give tangents of gradient 2 to the circle x^2 +y^2 =20.
    I have got the equation as 5x^2 + 4xc +c^2 -20=0 but don't know how to take it further. Please can you help.Thankyou.
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
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    #2

    Feb 7, 2010, 03:37 PM

    You are good so far. The discriminant is

    From the derived equation, we have:



    Solve for c and sub into 2x+c. There will be two values of course.
    Alice22's Avatar
    Alice22 Posts: 3, Reputation: 1
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    #3

    Feb 7, 2010, 04:57 PM

    Thank you so much. I knew it was b^2-4ac but I could not decide which was a,b, and c. Am I right in thinking c is 5 or -5?
    Alice22's Avatar
    Alice22 Posts: 3, Reputation: 1
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    #4

    Feb 7, 2010, 05:20 PM

    Sorry 10 or -10 (not 5)
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
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    #5

    Feb 7, 2010, 05:46 PM

    Yep, that's it. 2x-10 and 2x+10
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