Question: Let P be a moving point in the rectangular coordinate plane such that P is equidistant from the point A(0,4) and B(4, 0). Denote

Let P be a moving point in the rectangular coordinate plane such that P is equidistant from the point A(0,4) and B(4, 0). Denote the locus of P by r. A circle C passes through A and B and cuts the x-axis at another point N, such that BN is equal to the x-coordinate of the centre of the circle C. (b) Sketch the locus of r in the box provided below. Hence, describe the geometric relationship between I and AB. (3 marks) Find the equation of (1) r; (ii) C. (6 marks)

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