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**Question**

27) The line *y* = 3*x* + *p * and the circle *x*^{2} + *y*^{2} = 53 intersect at points *A* and *B*. *p* is a positive integer.

27 a) Show that the *x*-coordinates of points *A* and *B* satisfy the equation

10*x*^{2} + 6*px* + *p*^{2} – 53 = 0

**[3 marks]**

27 b) The coordinates of

Work out the coordinates of

You

*A*are (2, 7)Work out the coordinates of

*B*.You

**must**show your working.**[5 marks]**