Question

Find the centre of the circle passing through (2, 1), (5, - 8) and (2, - 9).

Answer 1

Answer:

Since, a circle is passing through the given point as A(5,-8),  B(2,-9) and C(2,1).

We have to find the centre of the given circle with unknown radius.

Let the centre be on O (x ,y)

Now, we will be approaching by making the distance of pomts from the centre as equal.

Distance of AO would be

Distance of BO would be

Distance of CO would be

Now,

Since AO = BO...........(1)       and             AO=CO...........(2)

Taking (1);

AO-BO

⇒

4x + y =2.............(3)

Now taking eq (2);

AO =CO

x - 3y = 14...........(4)

Equating (3) and (4), we get;

By solving we get x = 20/13   and y = -54/13

Answer 2

Answer:

Since, a circle is passing through the given point as A(5,-8),  B(2,-9) and C(2,1).

We have to find the centre of the given circle with unknown radius.

Let the centre be on O (x ,y)

Now, we will be approaching by making the distance of pomts from the centre as equal.

Distance of AO would be

Distance of BO would be

Distance of CO would be

Now,

Since AO = BO...........(1)       and             AO=CO...........(2)

Taking (1);

AO-BO

⇒

4x + y =2.............(3)

Now taking eq (2);

AO =CO

x - 3y = 14...........(4)

Equating (3) and (4), we get;

By solving we get x = 20/13   and y = -54/13