A) \[\frac{16}{5}\]
B) \[\frac{\sqrt{10025}}{25}-1\]
C) \[\frac{\sqrt{10125}}{25}-1\]
D) 24
Correct Answer: A
Solution :
\[{{z}_{1}}\] lies on the line segemtn joining the point 8 and 6i, equation of the line is \[\frac{x}{8}+\frac{y}{6}=1\]. ?(i) Slope is \[-\frac{6}{8}=-\frac{3}{4}\]. A line is perpendicular to the line \[\frac{x}{8}+\frac{y}{4}=1\] and passing through the point \[(1,\,0)\] is \[y-0=\frac{4}{3}\,(x-1)\] \[\Rightarrow \] \[4x-3y=4\] Point of intersection of lines (i) and (ii) is \[\left( \frac{88}{25},\,\,\frac{84}{25} \right)\] Min value of \[|z-{{z}_{1}}|\] is \[=\,\sqrt{{{\left( 1-\frac{88}{25} \right)}^{2}}+{{\left( 0-\frac{84}{25} \right)}^{2}}}-1\] \[=\sqrt{{{\left( \frac{63}{25} \right)}^{2}}\times \,{{\left( \frac{84}{25} \right)}^{2}}}-1\] \[=\frac{\sqrt{11025}}{25}-1=\frac{105}{25}-1\] \[=\frac{80}{25}=\frac{16}{5}\]You need to login to perform this action.
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