Question

A pair of straight lines drawn through the origin form an isosceles right angled triangle with the line 2x + 3y = 6, then the lines and the area of the triangle thus formed is

• A. x-5y=0
  5x+y=0
  
• B. 3x-y=0
  x+3y=0
  
• C. 5x-y=0
  x+5y=0
  
• D. None of these

Answer 1

The correct option is A x-5y=0

5x+y=0


y = mx. It makes an angle of $\pm {45}^{\circ }$ with 2x+3y=6
$\therefore tan(\pm {45}^{\circ })=\frac{m-(-2/3)}{1+m\left(2/3\right)}=\pm 1$
or $3m+2=\pm (3-2m)\Rightarrow m=\frac{1}{5},-5$
Hence sides are
x – 5y = 0
5x + y = 0
and 2x + 3y = 6
Solving in pairs, vertices are (0, 0),
$(\frac{6}{13},\frac{30}{13}),(\frac{30}{13},-\frac{6}{13})\Delta =\left|\frac{1}{2}\right(x_1{y}_2-x_2{y}_1\left)\right|=\frac{1}{2}\times \frac{936}{169}=\frac{36}{13}$