Question

the point of (3,-4) is the centre os a circle.If AB is the diameter of the circle and B is (5,-6) find the coordinates of A.

Answer 1

Answer: Given:-

A circle with centre (2,−3) and AB is the diameter of circle with B(1,4).

To find:- Coordinate of point A.

Let (x,y) be the coordinate of A.

Since AB is the diameter of the circle, the centre will be the mid-point of AB.

now, as centre is the mid-point of AB.

x-coordinate of centre =

2

x+1

y-coordinate of centre =

2

y+4

But given that centre of circle is (2,−3).

Therefore,

2

x+1

=2⇒x=3

2

y+4

=−3⇒y=−10

Thus the coordinate of A is (3,−10).

Hence the correct answer is (3,−10).