Question

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If AB is a diameter of circle C(0,r) where coordinates of a and b are (5,6) and (3,2) respectively then find the coordinates of O​

Answer 1

Explanation:

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).

Answer 2

Answer:

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 =2x+1

y-coordinate of centre =2y+4

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

Therefore,

2x+1=2⇒x=3

2y+4=−3⇒y=−10

Thus the coordinate of A is (3,−10).

Hence the correct answer is (3,−10)