Straight Line Question 81
Question: A pair of straight lines drawn through the origin form with the line $ 2x+3y=6 $ an isosceles right angled triangle, then the lines and the area of the triangle thus formed is [Roorkee 1993]
Options:
A) $ x-5y=0 $ $ 5x+y=0 $ $ \Delta =\frac{36}{13} $
B) $ 3x-y=0 $ $ x+3y=0 $ $ \Delta =\frac{12}{17} $
C) $ 5x-y=0 $ $ x+5y=0 $ $ \Delta =\frac{13}{5} $
D)None of these
Correct Answer: A $ \Rightarrow m=\frac{1}{5},-5 $ Hence sides are $ x-5y=0, $ $ 5x+y=0 $ and $ 2x+3y=6 $ . Solving in pairs, vertices are $ (0,0) $ , $ ( \frac{6}{13},\frac{30}{13} ),( \frac{30}{13},-\frac{6}{13} ) $ . $ \Delta =| \frac{1}{2}(x_1y_2-x_2y_1) |=\frac{1}{2}\times \frac{936}{169}=\frac{36}{13} $ .
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Answer:
Solution:
BETA
