Question

A straight line L is perpendicular to the line $5x-y=1.$ The area of the triangle formed by the line L and coordinate axes is 5. Find the equation of the line:

• A. $x+5y=\pm 5\sqrt{2}$
• B. $x-3y=0$
• C. $2x+y=0$
• D. $x+4y=5\sqrt{2}$

Answer 1

The correct option is A $x+5y=\pm 5\sqrt{2}$

$5x-y=1y=5x-1m=5m\prime =\frac{-1}{5}△AOB=\frac{1}{2}\times c\times 5c=\frac{5c^2}{2}$
We know $△AOB=5sq.unite\frac{1}{2}5c^2=5c=\pm \sqrt{2}y=-\frac{1}{5}x\pm \sqrt{2}5y=-x\pm 5\sqrt{2}x+5y=\pm 5\sqrt{2}$