What is the value of x If the points a 43 and bx5 are on the circle with Centre o Two Three?

If the points A(4, 3) and B(x, 5) lie on a circle with centre O(2, 3), find the value of x.

Question:

If the points A(4, 3) and B(x, 5) lie on a circle with centre O(2, 3), find the value of x.

Solution:

Given, the points A(4, 3) and B(x, 5) lie on a circle with centre O(2, 3).
Then OA = OB
Also (OA)2 = (OB)2

$\Rightarrow(4-2)^{2}+(3-3)^{2}=(x-2)^{2}+(5-3)^{2}$

$\Rightarrow(2)^{2}+(0)^{2}=(x-2)^{2}+(2)^{2}$

$\Rightarrow 4=(x-2)^{2}+4$

$\Rightarrow(x-2)^{2}=0$

$\Rightarrow x-2=0$

$\Rightarrow x=2$

Therefore, x = 2.

If the point A (4,3) and B ( x,5)  lies on a circle with the centre o (2,3) . Find the value of x.

Given, the points A(4,3) and B(x,5)  lie on a circle with center o(2,3) . Then OA = OB

Also `(OA)^2 = (OB)^2`

`⇒(4-2)^2 + (3-3)^2 = (x-2) ^2 +(5-3)^2`

`⇒(2)^2+(0)^2=(x-2)^2 +(2)^2`

`⇒ 4=(x-2)^2 +4`

`⇒(x-2)^2 =0`

⇒ x -2 = 0

⇒ x =2

Therefore,  x= 2

Concept: Coordinate Geometry

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