Circles

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