### MCQ's collected from all Engineering Entrance Examinations (Click here)

### Important Formulas:

**Standard Forms of a Circle:**

12. For circle , parametric equation is

General Equation of a circle:

13. The general equation of a circle is given by whose centre of the circle

14. Radius of the circle

15. If , then the radius of the circle is real and hence the circle is also real.

16. If , then the radius of the circle is and the circle is known as point circle.

17. If , then the radius of the circle is imaginary. Such a circle is imaginary, which is not possible to draw.

Position of a Point with Respect to a Circle:

18. A point lies outside on or inside a circle according as where

19. Intercepts on the Axes: The length of the intercepts made by the circle with and - axis are and

20. If then the roots of the equation are real and distinct, so the circle meets the in two real and distinct points.

21. If , then the roots of the equation are real and equal, so the circle touches axis, then intercept on axis is

22. If , then the roots of the equation are imaginary, so the given circle does meet axis in real point. Similarly, the circle cuts the axisin real and distinct points touches or does not meet in real point according

Equation of tangent: A line which touch only one point of a circle.

23. Point form the equation of the tangent at the point to a circle is

24. Point form the equation of the tangent at the point to a circle is .

25. Slope form The equation of the tangent of slope to the circle are

26. Slope form the equation of the tangents of slope to the circle are and the coordinates of the points of contact are

27. Slope form The equation of the tangents of slope to the circle are and the coordinates of the point of contact are

28. Parametric from the equation of the tangent to the circle at the point is .

Equation of normal: A line which is perpendicular to the tangent is known as a normal.

29. Point form : The equation of normal at the point to the circle is or

30. Point form : The equation of normal at the point to the circle is

31. Slope form: The equation of a normal of slope to the circle is .

32. Para metric form: the equation of normal to the circle at the point is or

33. The line meets the circle in unique real point ot touch the circle , if

and the point of contacts are

34. The line touches the circle , if .

35. The point of intersection of the tangent at the points and on the circle is given by

and

36. Power of a point with respect to the circle is .

Pair of tangents:

37. The combined equation of the pair of tangents drawn from a point to the circle is

or

where, and

38. The length of the tangents from the point to the circle is equal to

39. Chord of contact of two tangents, drawn from to the circle is or Similarly, for the circle is

40. Equation of chord Bisected at a Given point The equation of chord of the circle bisected at the point is given by i.e

41. Director Circle The locus of the point of intersection of two perpendicular tangents to a given circle is called a director circle. For circle , the equation of director of director circle is .

42. Common Chord The chord joining the points of intersection of two given circles is called common chord. If and be two circle, such that and , then their common chord is given by

43. Common Chord The chord joining the points of intersection of two given circles is called common chord. If denote the centre of the given circles, then their common chord

44. Common Chord The chord joining the points of intersection of two given circles is called common chord. If and be the radii of two circles, then length of common chord is

45. Angle of intersection of two circles

for_CIRCLES