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Maths Circle Problem watch

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    I'm really stuck on this maths question and don't know how to work it out. The question is y= -3x+c is a tangent to the circle x^2+y^2-4x-2y-5=0. Find c. Can anyone help? Thanks
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    (Original post by issyafd1)
    I'm really stuck on this maths question and don't know how to work it out. The question is y= -3x+c is a tangent to the circle x^2+y^2-4x-2y-5=0. Find c. Can anyone help? Thanks
    Substitute y=x+c into the equation of the circle and rearrange to get a quadratic equation set to 0.
    Then as the line is a tangent to the curve, the discriminant will be 0. So if you do b^2 -4ac which is the discriminant and set it =0 you will form a quadratic in terms of c and so you can then solve.
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    thank you so much :-). I subbed the equation of a line into the equation of the circle and got 10x^2-6cx+c^2+2x+c-5 but am not sure what would be a,b,c?
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    (Original post by issyafd1)
    thank you so much :-). I subbed the equation of a line into the equation of the circle and got 10x^2-6cx+c^2+2x+c-5 but am not sure what would be a,b,c?
    If you factorise for each term x^2, x and the constant term, you would get (assuming what you have written is correct) 10x^2 +2(1-3)x+c^2+c-5=0
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    Thank You
    So would a be 10x^2, b be 2(1-3)x and c be c^2+c-5 ?
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    (Original post by issyafd1)
    Thank You
    So would a be 10x^2, b be 2(1-3)x and c be c^2+c-5 ?
    Yes.
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    Thank you so much :-)
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    (Original post by issyafd1)
    Thank you so much :-)
    What did you get for the equation of the tangents in the end?
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    (Original post by issyafd1)
    I'm really stuck on this maths question and don't know how to work it out. The question is y= -3x+c is a tangent to the circle x^2+y^2-4x-2y-5=0. Find c. Can anyone help? Thanks
    http://www.thestudentroom.co.uk/forumdisplay.php?f=38
 
 
 
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