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    Hey!
    I have been sat here trying this question for at least 2 hours and tried everything I can think of...any ideas? (it's part b I am stuck on, but I will put entire question up)

    Question: The circle C has centre A and equation x^2+y^2+4x-8y+10=0
    a)find the coordinates of A and the radius of C
    b)The line L has equation x-3y+4=0
    Show that L is a tangent to circle C
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    (Original post by alicebrr)
    Hey!
    I have been sat here trying this question for at least 2 hours and tried everything I can think of...any ideas? (it's part b I am stuck on, but I will put entire question up)

    Question: The circle C has centre A and equation x^2+y^2+4x-8y+10=0
    a)find the coordinates of A and the radius of C
    b)The line L has equation x-3y+4=0
    Show that L is a tangent to circle C
    to show that something is a tangent you must put the equation of the line into the equation of the circle and show that it only meets the circle at one point. If this is the case it will usually factorize into 2 identical brackets
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    (Original post by alicebrr)
    Hey!
    I have been sat here trying this question for at least 2 hours and tried everything I can think of...any ideas? (it's part b I am stuck on, but I will put entire question up)

    Question: The circle C has centre A and equation x^2+y^2+4x-8y+10=0
    a)find the coordinates of A and the radius of C
    b)The line L has equation x-3y+4=0
    Show that L is a tangent to circle C
    so for part b i would make y the subject of the equation of the line, put it into the equation of the circle, expand and simplify, make it equal 0 and it should factorise into 2 identical brackets from which you can say that because there is only 1 solution that it is a tangent
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    part a)

    expand

    ( x - a )2 + ( y - b )2 = r2

    and compare to your version to find a,b,r
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    (Original post by Bored123454321)
    so for part b i would make y the subject of the equation of the line, put it into the equation of the circle, expand and simplify, make it equal 0 and it should factorise into 2 identical brackets from which you can say that because there is only 1 solution that it is a tangent
    Got you! So it would be something like this...? Yes?
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    (Original post by alicebrr)
    Got you! So it would be something like this...? Yes?
    ^^ looks about right
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    (Original post by thefatone)
    ^^ looks about right
    Thank you! I had that part at least an hour ago ahh
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    To show tangency, just show that the discriminant of the quadratic formed is 0  \Rightarrow line is tangent to curve.
 
 
 
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