Question

Formula to calculate points on a circle given radius and centre of circcle

Answer 1

Equation of a Circle

A circle is the set of all points in a plane at a given distance (called the radius ) from a given point (called the center.)



A line segment connecting two points on the circle and going through the center is called adiameter of the circle.

Assume that (x,y)(x,y) are the coordinates of a point on the circle shown. The center is at (h,k)(h,k) , and the radius is rr .



Use the Distance Formula to find the equation of the circle.

(x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−√=d(x2−x1)2+(y2−y1)2=d

Substitute (x1,y1)=(h,k),(x2,y2)=(x,y)(x1,y1)=(h,k),(x2,y2)=(x,y)and d=rd=r .

(x−h)2+(y−k)2−−−−−−−−−−−−−−−√=r(x−h)2+(y−k)2=r

Square each side.

(x−h)2+(y−k)2=r2(x−h)2+(y−k)2=r2

The equation of a circle with center (h,k)(h,k) and radius rr units is (x−h)2+(y−k)2=r2(x−h)2+(y−k)2=r2 .