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Q.

If the points $A (4, 3)$ and $B (x, 5)$ and are on the circle with center $O (2, 3),$ are on the circle with center then the value of $x$ then the value of is ____.

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Detailed Solution

If the points

A (4, 3)

and

B (x, 5)

are on the circle with center

O (2, 3),

then the value of

x

is 2.
We have been given,
The points

A (4, 3)

and

B (x, 5)

are on the circle.
O(2,3) is the center of the circle.
Now it is clear that one of the circumferential points and the center point share the same y coordinate.
The radius is therefore 2 units.
Using the distance formula between point B and the center of the circle,

D = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}

Substituting

x_{2} = x, x_{1} = 2, y_{2} = 5, and y_{1} = 3

, in the formula,

\Rightarrow \sqrt{{(x - 2)}^{2} + {(5 - 3)}^{2}}

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

\Rightarrow x = 2

Therefore, the value of ‘x’ is 2.

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