By Gutierrez J., Shpilrain V., Yu J.-T. (eds.)
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Extra resources for Affine Algebraic Geometry
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).  (i) Find the coordinates of the centre C of the circle.  (ii) Find the radius of the circle.  (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.   (v) Prove that the line AB is perpendicular to the line CD.
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. (iii) Find the equation of the tangent to the circle at the point P.    7. The coordinates of four points are P (-2, -1), Q (6, 3), R (9, 2) and S (1, -2).  (i) Calculate the gradients of the lines PQ, QR, RS and SP.  (ii) What name is given to the quadrilateral PQRS?  (iii) Calculate the length SR.
Iv) Show that the equation of SR is 2y = x – 5 and find the equation of the line L through Q perpendicular to SR.   (v) Calculate the coordinates of the point T where the line L meets SR.  (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).  (i) Find the coordinates of the centre C of the circle.  (ii) Find the radius of the circle.  (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.