SAEP Matric Success – Zisukhanyo Maths Worksheet

Tuesday 21st April 2009

Circles

1. Given: A circle with equation x2 + y2 = 50.a) Determine the co-ordinates of the x-intercepts of the circle (Leave answers in surd form)b) Calculate the co-ordiantes of the points of intersection of the line x – y – 6 = 0 and the circle.

2. Draw sketch graphs of the following equations and show at least one point on the circle:a) x2 + y2 = 9 b) x2 + y2 = 50c) y2 = 5 – x2 d) y2 = 16 – x2

3. Determine the equation of the circle with the centre at the origin, and:a) a radius of 3 units b) a radius of √7 unitsc) a radius of 3√2 units d) passing through the point (-2 ; 3)e) passing through the point (3 ; 1) f) passing through the point (-4 ; -2)

4. (3 ; a) is a point on the circle x2 + y2 = 18. Determine the 2 possible values of a.

5. Determine the equatiuon of the circle ith centre:a) (2 ; 10) and radius of 4 units b) (-1 ; 1) and radius of √3 unitsc) (-2√5 ; 4) and passing through the origin d) (3 ; -5) and passing through (-1 ; 1)e) (a ; b) and radius of 3 units f) (-2 ; 4) and radius of r units

6. Determine the equation of a circle with a radius of 5 units which cuts the x-axis at P(1 ; 0) and Q(7 ; 0) respectively.

7. Given the circle x2 + y2 – 6x - 2y + 1 = 0.a) Determine the co-ordinates of the centre of the circle, and the length of the radius.b) Calculate the length of a tangent from a point A(t ; 7) to the point P on the circumference of the circle, is 2√13.