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). $\Rightarrow(4-2)^{2}+(3-3)^{2}=(x-2)^{2}+(5-3)^{2}$ $\Rightarrow(2)^{2}+(0)^{2}=(x-2)^{2}+(2)^{2}$ $\Rightarrow 4=(x-2)^{2}+4$ $\Rightarrow(x-2)^{2}=0$ $\Rightarrow x-2=0$ $\Rightarrow x=2$ 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 Is there an error in this question or solution? |