A) \[\frac{23}{\sqrt{15}}\]
B) \[\sqrt{17}\]
C) \[\frac{17}{\sqrt{15}}\]
D) \[\frac{23}{\sqrt{17}}\]
Correct Answer: D
Solution :
\[\frac{x}{5}+\frac{y}{b}=1\] Passes through (13, 32) \[\frac{13}{5}+\frac{32}{b}=1\] \[\Rightarrow \] \[13b+160=5b\] \[\Rightarrow \]\[b=-20\] so line is \[20x+5y=100\] (1) second line \[\frac{x}{c}+\frac{y}{3}=1\] \[3x+cy=3c\] (2) (1) and (2) are parallel \[\frac{3}{-20}=\frac{c}{5}\] \[c=\frac{-3}{4}\] Line \[3x-\frac{3}{4}y=-\frac{9}{4}\] \[12x3y=9\] \[-20x+5y=-9\times \left( -\frac{5}{3} \right)\] \[-20x+5y=15\] ......(2) Distance between (1) and (2) \[=\frac{|-100-15|}{\sqrt{400+25}}=\frac{115}{\sqrt{425}}=\frac{115}{5\sqrt{17}}=\frac{23}{\sqrt{17}}\]
You need to login to perform this action.
You will be redirected in
3 sec
