Download MEI C1 Study Resources Core1 Co-ordinate Geometry 2 Curves by Roger Porkess PDF

By Roger Porkess

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Additional resources for MEI C1 Study Resources Core1 Co-ordinate Geometry 2 Curves And Circles

Example text

The coordinates of four points are P (-2, -1), Q (6, 3), R (9, 2) and S (1, -2). [4] (i) Calculate the gradients of the lines PQ, QR, RS and SP. [1] (ii) What name is given to the quadrilateral PQRS? [2] (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. [5] [3] (v) Calculate the coordinates of the point T where the line L meets SR. [3] (vi) Calculate the area of the quadrilateral PQRS. 8. AB is the diameter of a circle.

Describe fully the curve whose equation is x 2 + y 2 = 4 . [2] 3. The coordinates of two points are A (-1, -3) and B (5, 7). Calculate the equation of the perpendicular bisector of AB. [4] 4. 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.

1] (ii) What name is given to the quadrilateral PQRS? [2] (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. [5] [3] (v) Calculate the coordinates of the point T where the line L meets SR. [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.

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