Equation of Circle in Diameter form
Let AB the diameter of the circle with center O where A(x1, y1) and B(x2, y2) are the end-points of the diameter. Let P be any point on the circumference of the circle. Then, AP and BP is joined su...
Circle
1. When the center of circle is origin.
→x2+y2 = r2
2. When the center of circle is (h, k).
→(x-h)2+(y-k)2 = r2 ..................(i)
3. When the circle touches x-axis.
If the circle touches x-axis then, r=k and putting the value in equation (i)
→(x-h)2+(y-k)2 = k2
4. When the circle touches y-axis.
If the circle touches y-axis then, r=h and putting the value in equation (i)
→(x-h)2+(y-k)2 = h2
5.When the circle touches both axes.
If the circle touches both axes then, r=h=k and putting the value in equation (i)
→(x-h)2+(y-h)2 = h2
OR,
→(x-k)2+(y-k)2 = k2
OR,
→(x-r)2+(y-r)2 = r2
6. When the circle passes through origin.
If the circle passes through origin then, r2=h2+k2 and putting the value in equation (i)
→(x-h)2+(y-k)2= h2+k2