## Sections in the chapter

1. Definition

2. Standard equation of a circle

3. Some particular cases of the central form of the equation of a circle

4. General equation of a circle

5. Equation of a circle when the co-ordinates of end points of a diameter are given

6. Intercepts on the axis

7. Position of a point with respect to a circle

8. Equation of a circle in parametric form

9. Intersection of a straight line and a circle

10. The length of the intercept cut off from a line by a circle

11. Tangent to a circle at a given point.

12. Normal to a circle at a given point

13. Length of the tangent from a point to a circle

14. Pair of tangents drawn from a point to a given circle

15. Combined equation of pair of tangents

16. Director circle and its equation

17. Chord of contact of tangents

18. Pole and polar

19. Equation of the chord bisected at a given point

20. Diameter of a circle

21. Common tangents to two circles

22. Common chord of two circles

23. Angle of intersection of two curves and the condition of orthogonality of two circles.

24. Radical axis

25. Equation of a circle through the intersection of a circle and line

26. Circle through the intersection of two circles

27. Coaxial system of circles

## Revision Points

Equation of circle in various forms

a. Centre (h,k) and radius a

b. Centre (h,k) and passing through origin

c. Centre (h,k) and circle touches the axis of x

d. Centre (h,k) and circle touches the axis of y

e. Centre (h,k) and and circle touches both axes.

f. general equation

g. circle whose diameter is the line joining two points

h. Circle through three given points

i. Parametric equation of the circle

h. equation of a circle that touches given circle at a given point

j. Equation of a circle passing through the intersection of given circles S1 = 0 and S2 = 0

The standard equation of a circle with center C(h,k) and radius r is as follows:

(x - h)² + (y - k)² = r²

Parametric Equations

The equation of a circle, centred at the origin, is: x2 + y2 = a2, where a is the radius.

Suppose we have a curve which is described by the following two equations:

x = acosθ (1)

y = asinθ (2)

We can eliminate q by squaring and adding the two equations:

x² + y² = a²cos²θ + a²sin²θ = a² .

Hence equations (1) and (2) together also represent a circle centred at the origin with radius a and are known as the parametric equations of the circle. θ is known as the parameter. As θ varies between 0 and 2π, x and y vary.

http://www.mathsrevision.net/alevel/pages.php?page=97

Updated 17 Jan 2016, 28 April 2008

## No comments:

Post a Comment