that is bisected at point (5, 3) is:
A)
B)
C)
D) None of these
Correct Answer: B
Solution :
The equation of the chord, having mid-point as \[\left( {{\operatorname{x}}^{2}},\,\,{{y}^{2}} \right)\] of the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] is given by \[T={{S}_{1}}\] ?. (i) where, \[T=\frac{x{{x}_{1}}}{{{a}^{2}}}-\frac{y{{y}_{1}}}{{{b}^{2}}}-1\,\,and\,\,{{S}_{1}}=\frac{x_{1}^{2}}{{{a}^{2}}}-\frac{y_{1}^{2}}{{{b}^{2}}}-1\] According to the question, \[({{x}_{1}},\,\,{{y}_{1}})=(5,\,\,3)\,\,and\,\,{{a}^{2}}=16,\,\,{{b}^{2}}=25\] as \[25{{x}^{2}}-16{{y}^{2}}=400\] \[\Rightarrow \,\,\,\frac{{{x}^{2}}}{16}-\frac{{{y}^{2}}}{25}=1\] \[\therefore \,\,\,\,\frac{5x}{16}-\frac{3y}{25}=\frac{25}{16}-\frac{9}{25}\] [Using (i)] \[\Rightarrow \,\,\,\,125x -48y=625 -144\] \[\Rightarrow \,\,\,125x-48y=481\]
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