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    Two circles, A and B, touch each other at exactly one point...

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    Two circles, A and B, touch each other at exactly one point, as shown in the diagram below. The equation of circle A is . Circle B has centre (1, k + 1) and radius 4.

    Please see the attached file for the fully formatted problems.

    (Not to scale)

    i) Find the completed square form of x2 - 18x
    Find the completed square form of y2 - 2y

    ii) Use your answer from part i) to express the equation of circle A in the form
    (x - a)2 + (y - b)2 = r2

    iii) write down the centre and radius of circle A.

    i) Explain why the distance between the centres of circles A and B is 10.

    ii) Express this distance also in terms of k, and hence find the two possible values of k.

    iii) Hence show that the two possible equations of circle B are


    c) Show algebraically that the line y = 4/3 x - 1 is a tangent to circle A, and give the coordinates of the point of contact.

    (You should work with fractions in this part of the question)

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