Question

Find the equation of the circle whose diameter is the join of the points: (1,3), (4,5)

Answer 1

Coordinates of the centre of the circle is, x=x1 + (x2 - x1)/2 = 1 + (4 - 1)/2 = 2.5

                                                                     y=y1 + (y2 - y1)/2 = 3 + (5 - 3)/2 = 4

Therefore, (2.5,4) are the coordinates of the point liying on the centre of the circle.

Now, We have to find the radius.

For that we need to find the length of the segment situated between the central point and any two end points, i.e. , (2.5,4) and (1,3) or (4,5)

The length = $\sqrt{(2.5 - 1)^{2} + (4 - 3)^{2}}$

                   = $\sqrt{(1.5)^{2} + (1)^{2}}$

                   = $\sqrt{3.25}$

or Radius, r = $\sqrt{3.25}$

Now. Area of the circle = π$r^{2}$

                                       = 3.14 * 3.25

                                       = 10.20500...

                                       = 10.2 (approx.)

Answer: Area of the circle is 10.2 .