A) (2, 0)
B) (12, -5)
C) (5, -12)
D) None of the above
Correct Answer: C
Solution :
Let, AB be the diameter and C be the centre of the circle. Let coordinates of A be (a, b). Clearly, C will be the mid-point of AB. |
\[\therefore\]Coordinates of \[C=\left( \frac{a+1}{2},\,\frac{b+4}{2} \right)\] |
\[\left[ \because \,\,mid\,-\,po\operatorname{int}=\left( \frac{{{x}_{1}}+{{x}_{2}}}{2},\frac{{{y}_{1}}+{{y}_{2}}}{2} \right) \right]\] |
\[\Rightarrow \,\,\,\left( 3,\,\,-4 \right)=\left( \frac{a+1}{2},\frac{b+4}{2} \right)\] |
[given, coordinates of C = (3, - 4)] On comparing the coordinates of x and y from both sides, we get |
\[\frac{a+1}{2}=3\] and \[\frac{b+4}{2}=-4\] |
\[\Rightarrow a+1=6\] and \[b+4=-8\] |
\[\Rightarrow \,\,\,a=5\] and \[b=-12\] |
Hence, the coordinates of point |
A are (5, -12). |
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