A) \[{{m}_{1}}+{{m}_{2}}=-\frac{24}{11}\]
B) \[{{m}_{1}}{{m}_{2}}=\frac{20}{11}\]
C) \[{{m}_{1}}+{{m}_{2}}=\frac{48}{11}\]
D) \[{{m}_{1}}{{m}_{2}}=\frac{11}{20}\]
Correct Answer: B
Solution :
The equation of a line passing through (6, 2) is \[y-2=m(x-6)\] \[\Rightarrow \] \[y=mx+2-6m\] Since, this line is tangent to the given hyperbola. \[\therefore \] \[{{(2-6m)}^{2}}=25{{m}^{2}}-16\] \[\Rightarrow \] \[36{{m}^{2}}+4-24m-25{{m}^{2}}+16=0\] \[\Rightarrow \] \[11{{m}^{2}}-24m+20=0\] Let\[{{m}_{1}}\]and\[{{m}_{2}}\]are the roots of the above equation. \[\therefore \] \[{{m}_{1}}+{{m}_{2}}=\frac{24}{11}\]and \[{{m}_{1}}{{m}_{2}}=\frac{20}{11}\]
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