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9.Straight Line
hard
ચોરસના એક વિર્કણનું સમીકરણ $8x - 15y = 0$ હોય અને તેનું એક શિરોબિંદુ $(1, 2)$ છે. આપેલ શિરોબિંદુમાંથી પસાર થતી બાજુના સમીકરણ મેળવો.
A
$23x + 7y = 9,\;7x + 23y = 53$
B
$23x - 7y + 9 = 0,\;7x + 23y + 53 = 0$
C
$23x - 7y - 9 = 0,\;7x + 23y - 53 = 0$
D
એકપણ નહી.
(IIT-1962)
Solution
(c) Slope of $BD$ is $\frac{8}{{15}}$ and angle made by $BD$ with $AD$ and $DC$ is ${45^o}$. So let slope of $DC$ be m, then $\tan {45^o} = \pm \frac{{m – \frac{8}{{15}}}}{{1 + \frac{8}{{15}}m}}$
$ \Rightarrow (15 + 8m) = \pm (15m – 8)$
==> $m = \frac{{23}}{7}$and $ – \frac{7}{{23}}$
Hence the equations of $DC$ and $AD$ are
$y – 2 = \frac{{23}}{7}(x – 1)$$ \Rightarrow 23x – 7y – 9 = 0$
and $y – 2 = – \frac{7}{{23}}(x – 1)$$ \Rightarrow 7x + 23y – 53 = 0$.
Standard 11
Mathematics
