# If the diameter of a circle has endpoints A(7, 2) and B(-1, 8), where is the center of the circle?

##### 1 Answer

Centre of the circle lies at :

#### Explanation:

Suppose if **A** and **B** in a plane space, then the position vector of any point **C** along the line connecting the two points can be written as a parametric equation :

**X Component**:

**Y Component**:

If **C** from point **A** and **A** and **B**, then

**Solution**: We are given -

If **A** and **B** are the end points along the diameter then we know that the centre of the circle is the midpoint between the two. i.e

So

So the coordinates of the centre

Therefore

**Note**: You can verify the correctness of the solution by finding the distance between the centre and the two points and verify that they are at the same distance.

**A-C Distance**:

**B-C Distance**: