A) \[4,-\,\,5\]
B) \[-\,\,7,11\]
C) 3, 9
D) \[3,-\,\,10\]
Correct Answer: D
Solution :
Suppose, AB be a diameter of the circle having its centre at C \[(2,-\,\,3)\]and coordinates of end point B are (1, 4). |
Let the coordinates of A be (x, y) |
Since, AB is diameter. |
\[\therefore \]C is the mid-point of AB |
The coordinates of C are\[\left( \frac{x+1}{2},\frac{y+4}{2} \right)\] |
[\[\because \]Coordinate of mid \[-\] point |
\[\left. =\left( \frac{{{x}_{1}}+{{x}_{2}}}{2},\frac{{{y}_{1}}+{{y}_{2}}}{2} \right) \right]\] |
But it is given that the coordinates of C are \[(2,-\,\,3).\] |
\[\therefore \] \[\frac{x+1}{2}=2\]\[\Rightarrow \]\[x+1=4\] |
\[\Rightarrow \] \[x=3\]and \[\frac{y+4}{2}=-\,\,3\] |
\[\Rightarrow \] \[y+4=-\,\,6\] |
\[\Rightarrow \] \[y=-10\] |
So the required coordinates of A are \[(3,-\,\,10).\] |
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