Equations of the Circle

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Equations of the Circle

  1. 1. Analytical Geometry T- 1-855-694-8886 Email- info@iTutor.com By iTutor.com
  2. 2. Circle  A circle is the set of all points in a plane that are equidistant from a fixed point in the plane.  The fixed point is called the centre of the circle .  The distance from the centre to a point on the circle is called the radius of the circle Centre o A C B Radius OA = OB =OC © iTutor. 2000-2013. All Rights Reserved
  3. 3. Equation Of The Circle  The equation of the circle is simplest if the centre of the circle is at the origin.  But the equation of the circle with a given centre and radius Given C (h, k) be the centre and r the radius of circle. Let P(x, y) be any point on the circle Then, by the definition, | CP | = r . By the distance formula, X Y P (x , y) C (h, k) © iTutor. 2000-2013. All Rights Reserved
  4. 4. We have i.e., This is the required equation of the circle with centre at (h, k) and radius r rkyhx 22 222 rkyhx © iTutor. 2000-2013. All Rights Reserved
  5. 5. Examples Find the equation of the circle with centre (–3, 2) and radius 4. Solution: Here h= –3, k= 2 and r= 4. Therefore, the equation of the required circle is 1623 22 yx © iTutor. 2000-2013. All Rights Reserved
  6. 6. The End Call us for more Information: www.iTutor.com Visit 1-855-694-8886

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