Book Online Demo

Check Your IQ

Try Test

Courses

Offline Centres

Find the coordinates of a point A, where AB is the diameter of a circle, whose centre is $(4, - 3)$ and B is $(2, 6)$ .

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

A (6, - 12)

A (5, 10)

A (1, 2)

A (3, 1)

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

It is given that AB is the diameter of a circle, whose centre is

(4, - 3)

and B is

(2, 6)

.
Let the coordinates of the point A be

(x, y)

.
Let O be the centre.

⇒ O (4, − 3)

Thus, O is the midpoint of segment AB.
We know that, if the coordinates of two points are

x 1, y 1

and

x 2, y 2

then the coordinate of the middle point of the two points will be

x 1 + x 2 2, y 1 + y 2 2

.
Thus, using the midpoint formula,

(4, − 3) = x + 2 2, y + 6 2

For, x-coordinate,

4 = x + 2 2 ⇒ 4 × 2 = x + 2 ⇒ x = 6

For, y-coordinate,

− 3 = y + 6 2 ⇒ − 3 × 2 = y + 6 ⇒ y = − 12

Thus, the coordinates of the point are

A (6, − 12)

.
Hence, option (1) is correct.

Watch 3-min video & get full concept clarity