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Math Help - Solve the equations of these circles

  1. #1
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    Solve the equations of these circles

    The x-axis and the line y=8 are both tangents to a circle k.
    The centre of the circle lies on the line 2x-3y=0
    (i) Write down the length of the radius.
    (ii)Find the coordinates of the centre of the circle.
    (iii)Write down the equation of the circle.
    That is question 1
    Question 2:
    The y-axis and the line x=8 are tangents to a cricle.
    The centre of the circle lies on the line 2x-y-3=0.
    (i)Write down the length of the radius of the circle.
    (ii)Find the coordinates of the centre of the circle.
    (iii)Find the equation of the circle.
    Question 3
    A circle touches the y-axis at the point (0,-3) and it contains the point (4,1).
    Find the equation of this circle
    Question 4
    The x-axis and the line y=10 are tangents to a circle.
    If the circle also contains the point (1,5), find the equations of the two circles that satisfy these conditions.
    Thanks any help is much appreciated!!!
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  2. #2
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    Hello and welcome to MathHelpForum.
    You should understand that this is not a homework service nor is it a tutorial service. Please either post some of your own work on these problems or explain what you do not understand about the question. Moreover, we discourage posting a whole list of problems at one time, especially if you show no effort.
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  3. #3
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    Thank you for the advice.
    I have these questions solved but I do not know whether they are correct. Except for the last one.
    Question 1
    (i) 4
    (ii)Centre
    (iii)(x-6)^2+(y-4)^2+16
    Question 2
    (i)4
    (ii)(4,5)
    (iii) (x-4)^2+(y-5)^2=16
    Question 3
    Would the radius = 4
    would its equation be (x+3)^2+(y-4)^2=16

    And the last one I am stuck on?Would the radius be 2.5.I am not sure on how there can be two circles. I'll delete the thread if it's unsuitable but I did make an effort at solving them.
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  4. #4
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    For #4, it is clear that the radius is 5.
    And the center looks like (p,5).
    So what is p?
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  5. #5
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    Thanks I got it!!! p=-4 or 6
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