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    The circle C has centre A(4,3) and passes through the point B(10, 5) .

    (a) Find an equation for C.

    The line L1 is the tangent to C at the point B.

    (b) Find an equation for L1

    The line L2 is parallel to L1 and passes through the mid-point of AB.

    Given that intersects C at the points P and Q,

    (c) Find the length of PQ, giving your answer in its simplest surd form.
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    (Original post by HelpMeUnderstand)
    The circle C has centre A(4,3) and passes through the point B(10, 5) .

    (a) Find an equation for C.

    The line L1 is the tangent to C at the point B.

    (b) Find an equation for L1

    The line L2 is parallel to L1 and passes through the mid-point of AB.

    Given that intersects C at the points P and Q,

    (c) Find the length of PQ, giving your answer in its simplest surd form.
    Have you made any attempt or given it some thought?

    I'll start you off with a)
    We know what the centre is.
    We also know that it passes through B. Thus, B is a point on the circumference on the circle. What's the line between the centre of a circle and a point on the circumference? Radius.

    So now you can calculate the radius of the circle.
    You know how to calculate the length of a line when given two coordinates...
    Spoiler:
    Show
     \mathrm{For\ a\ distance,\ d} = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}

     \mathrm{Therefore\ AB} = \sqrt{(10-4)^2 + (5-3)^2} = \sqrt 40
    You also know the equation of a circle.
    So you can now answer a)
    Spoiler:
    Show
     \mathrm{For\ a\ circle\ with\ centre\ (a,b)\ and\ radius,\ r}: (x - a)^2 + (y - b)^2 = r^2
 
 
 

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