Question

The graph $y^2+2xy+40|x|=400$ divides the plane into regions. Then the area of bounded region is

• A. $200$ sq. units
• B. $400$ sq. units
• C. $800$ sq. units
• D. $500$ sq. units

Answer 1

Answer: (C)

$800$ sq. units

For $x<0$, the equation is
$(y-20)(y+2x+20)=0$
Hence, the area is $20\times 40=800$ sq. units.
For $x\ge 0$ the equation simplifies to $y^2-400+2xy+40x=(y-20)(y+20)+2x(y+20)=(y+20)(y+2x-20)=0$
Thus, obtained lines make a quadrilateral $ABCD,$
Area of quadrilateral $ABCD=2\times$ Area of triangle $BCD$$=2\times \frac{1}{2}\times$ base $\times$height$=20\times 40=800$ sq.units