Question

The triangle formed by the lines
$2x^2+3xy-2y^2=0,3x+y+1=0$ is

• A. isosceles
• B. right angled
• C. right angled isosceles
• D. equilateral

Answer 1

Answer: (C)

right angled isosceles

$2x^2+3xy-2y^2=0$

$t=\frac{x}{y},2t^2+3t-2=0$

$t=\frac{-3\pm \sqrt{9+16}}{4}$
$t=-2,\frac{1}{2}$
$y=\frac{-x}{2}$ & $y=2x$
$m_1=\frac{-1}{2}$ & $m_2=2$
So, $m_1{m}_2=-1$
$\therefore$ Triangle formed is isosceles triangle
$\Rightarrow 3x+y+1=0$ & $y=\frac{-x}{2}$
$\Rightarrow \frac{5x}{2}+1=0$
$\Rightarrow x=\frac{-2}{5},y=\frac{1}{5}$
$\Rightarrow 3x+y+1=0$ & $y=2x$
$\Rightarrow x=\frac{-1}{5},y=\frac{-2}{5}$
$\Delta ABC$ is isosceles right angle triangle.