Question

Find the co-ordinates of a point $A$, where $AB$ is the diameter of a circle, whose centre is $(2,-3)$ and $B$ is $(1,4)$.

Answer 1

Given, $AB$ is a diameter of circle, point $B$ is $(1,4)$ and centre of circle is $(2,-3)$

Let point $A$ is $(x,y)$

As we know mid point of diameter is centre of circle

$\therefore \frac{x+1}{2}=2$ and $\frac{y+4}{2}=-3$

$\Rightarrow x+1=4$ and $y+4=-6$

$\Rightarrow x=3,y=-10$

point $A$ is $(3,-10)$