Question

Find the coordinates of a point A , where AB is the diameter of a circle whose radius is (2,3) and B(1,4)

Answer 1

Let O be the centre of the circle.

Since AB is the diameter,O is the midpoint of AB

$o= ( \frac{x1 + x2}{2} ,\: \frac{y1 + y2}{2} ) \\ (2, - 3) = ( \frac{x + 1}{2} , \frac{y + 4}{2} ) \\ \frac{x + 1}{2} = 2 \\ x + 1 = 4$

$x = 4 - 1 = 3 \\ \frac{y + 4}{2} = - 3 \\ y + 4 = - 6 \\ y = - 6 - 4 = - 10$

A(3,-10)