M(—3 ; 4) is the centre of the large circle and a point on the small circle having centre O(0; 0). From N(—11 ; p), a tangent is drawn to touch the large circle at T with NT is parallel to the y-axis. NM is a tangent to the smaller circle at M with MOS a diameter.
4.1 Determine the equation of the small circle. (2)
4.2 Determine the equation of the circle centred at M in the form (x-a)2 + (y- b)2 =r2 (3)
4.3 Determine the equation of NM in the form y= mx +c (4)
4.4 Calculate the length of SN. (5)
4.5 If another circle with centre B(—2 ; 5) and radius k touches the circle centred at M, determine the value(s) of k, correct to ONE decimal place. (5)
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