By Earl Perry

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AB is the diameter of a circle. A is (1, 3) and B is (7, -1). [2] (i) Find the coordinates of the centre C of the circle. [2] (ii) Find the radius of the circle. [2] (iii) Find the equation of the circle. (iv) The line y + 5x = 8 cuts the circle at A and again at a second point D. Calculate the coordinates of D. [4] [3] (v) Prove that the line AB is perpendicular to the line CD.

3] (vi) Calculate the area of the quadrilateral PQRS. 8. AB is the diameter of a circle. A is (1, 3) and B is (7, -1). [2] (i) Find the coordinates of the centre C of the circle. [2] (ii) Find the radius of the circle. [2] (iii) Find the equation of the circle. (iv) The line y + 5x = 8 cuts the circle at A and again at a second point D. Calculate the coordinates of D. [4] [3] (v) Prove that the line AB is perpendicular to the line CD.

Show that the line y = 3x – 10 is a tangent to the circle x 2 + y 2 = 10 . [4] 5. The line y = 2 x − 3 meets the x-axis at the point P, and the line 3 y + 4 x = 8 meets the x-axis at the point Q. The two lines intersect at the point R. (i) Find the coordinates of R. [4] (ii) Find the area of triangle PQR. [3] 6. The equation of a circle is x 2 + y 2 − 4 x + 2 y = 15 (i) Find the coordinates of the centre C of the circle, and the radius of the circle. (ii) Show that the point P (4, -5) lies on the circle.