Circle Final Strategies
- 2. What do you need to know? How to find centre and radius of circle Finding equation of circle : (x-a) 2 + (y-b) 2 = r 2 Equation of tangent to circle at given point Proving tangency Do circles touch? Points of intersection (line & circle) Common tangent Midpoint of diameter is centre of circle
- 3. 1. Finding centre and equation of circle Time remaining 00 :00 Time remaining 00 :05 Time remaining 00 :10 Time remaining 00 :20 Time remaining 00 :30 Time remaining 01 :00 Time remaining 02 :00 Centre is (2, 2) Radius is 2 2 4 2 2 2 Centre B is (10, 6) Radius is 2 (identical to A) Time remaining 03 :00 Time remaining 04 :00
- 4. 2. Radius of circle Time remaining 00 :00 Time remaining 00 :05 Time remaining 00 :10 Time remaining 00 :20 Time remaining 00 :30 Time remaining 01 :00 Time remaining 02 :00 Time remaining 03 :00 For circle radius must be positive so: 2g = -6 2f = 4 g = -3 f = 2
- 5. 3. Equation of tangent Time remaining 00 :00 Time remaining 00 :05 Time remaining 00 :10 Time remaining 00 :20 Time remaining 00 :30 Time remaining 01 :00 Time remaining 02 :00 Time remaining 03 :00 Time remaining 04 :00 Equation thru (3,4) Gradient of radius: Gradient of tangent:
- 6. 4. Proving tangency / Common tangents 8 Marks Show that the line x + 2y = 3 is a tangent to the circle (b) Show that this tangent is also a tangent to the circle with equation To prove tangency sub in equation of line into equation of circle and show b 2 – 4ac = 0.
- 7. 4. Proving tangency / Common tangents 8 Marks Show that the line x + 2y = 3 is a tangent to the circle (b) Show that this tangent is also a tangent to the circle with equation To prove tangency sub on equation of line into equation of circle and show b 2 – 4ac = 0.
- 8. 4. Proving tangency / Common tangents 8 Marks Show that the line x + 2y = 3 is a tangent to the circle (b) Show that this tangent is also a tangent to the circle with equation In part (b) do exactly the same!!!!!!
- 9. 5. Points of intersection / Midpoint as centre To find points of intersection sub in line equation to circle equation So x = 6 or x = -2 A is x = 6 and so is (6, 6)
- 10. 5. Points of intersection / Midpoint as centre Centre of circle will be midpoint of AB Radius is distance from centre to A or B Equation of circle:
- 11. 5. Touching Circles 4 Marks (a) (i) Show that the radius of circle P is (ii) Hence show that circles P and Q touch. Circle P has equation Circle Q has centre (-2, -1) and radius
- 12. 5. Touching Circles Solution to (a)(i): If given general form of circle’s equation remember 2g = -8 g = -4 2f = -10 f = -5
- 13. 5. Touching Circles Solution to (a)(ii): If circles touch distance between centres =sum of lengths of radii g = -4 f = -5 Centre of P is (4, 5)