Coordinate Geometry

1. A line has equation .
   (a) Find the gradient of the line.
   (b) Find the equation of the line which is parallel to and passes through the point . Give your answer in the form .
2. The coordinates of two points are and . Calculate the equation of the perpendicular bisector of AB .
3. In this question you must show detailed reasoning.

The line does not intersect the circle .
Find the range of values for .
4. The equation of a circle is
(a) Find the coordinates of the centre C of the circle, and the radius of the circle.
(b) Show that the point lies on the circle.
Find the equation of the tangent to the circle at the point P .
5. The coordinates of four points are and .
(a) Prove that PQRS is a parallelogram.
(b) Find the perpendicular distance of Q from SR .
Calculate the area of the parallelogram PQRS .
6. AB is the diameter of a circle. A is and B is .
(a) Find the equation of the circle.
(b) The line cuts the circle at A and again at a second point D . Calculate the coordinates of D .
Find the area of triangle ABD .