Let C be the centre of a circle with coordinates (h,k). If radius of the circle is R , then equation of such a circle is given by (x-h)

You can enter the equations of above seven types in the input box at the near bottom of the following applet and see the changes in circle.

^{2}+ (y-k)^{2}= R^{2}. Here we will explore the changes in circle with the changes made in the values of h , k and R.- When the centre of the circle coincides with the origin i.e. h = k = 0 . Equation of the circle is x
^{2}+ y^{2}= R^{2} - When the circle passes through the origin i.e. R
^{2}= h^{2}+ k^{2}. Equation of the circle is (x-h)^{2}+ (y-k)^{2}= h^{2}+ k^{2}or x^{2}+ y^{2}– 2hx – 2 ky = 0. - When the circle touches x – axis i.e. R = k. Equation of the circle is (x-h)
^{2}+ (y-R)^{2}= R2 or x^{2}+ y^{2}– 2hx – 2Ry + h^{2}= 0 - When the circle touches y - axis i.e. R = h. Equation of the circle is (x-R)
^{2}+ (y-k)^{2}= R^{2}or x^{2}+ y^{2}– 2Rx – 2ky + k^{2}= 0 - When the circle touches both the axes i.e. R = h = k. Equation of the circle is (x-R)
^{2}+ (y-R)^{2}= R^{2}or x^{2}+ y^{2}– 2Rx – 2Ry + R^{2}= 0 - When the circle passes through the origin and centre lies on x-axis i.e. k = 0 and h = R. Equation of circle is (x-R)
^{2}+ (y-0)^{2}= R^{2}or x^{2}+ y^{2}– 2xR = 0 - When the circle passes through the origin and centre lies on y-axis i.e. h = 0 and k = R. Equation of circle is (x-0)
^{2}+ (y-R)^{2}= R^{2}or x^{2}+ y^{2}– 2yR = 0

You can enter the equations of above seven types in the input box at the near bottom of the following applet and see the changes in circle.

that helped a lot. thank you sir

ReplyDeleteI want to share my ideas about circle as circle making is a easy task just draw a curve in response to a fix line from a central point and all points are the the same distance from the center.

ReplyDelete(x-a)2 + (y-b)2 = r2 is standard equation of a circle. where r is radius.

tnk u sir. it helped me a lot.....

ReplyDeleteThank you Sir !

ReplyDeleteThanks for this but what when the circle passes through 2 points and his center lies in x-axis

ReplyDeleteThanks for this but what when the circle passes through 2 points and his center lies in x-axis

ReplyDelete