Question

The graph of $y^2+2xy+40\left(x\right)=400$ divides the plane into the regions. The area of the bounded region is

• A. $400$ sq. units
• B. $800$ sq.units
• C. $600$ sq. units
• D. None of these

Answer 1

The correct option is A $400$ sq. units

$y^2+2xy+40x=400$

$\Rightarrow y^2+2xy+x^2=x^2-40x+400$

$\Rightarrow (x+y{)}^2=(x-20{)}^2$

$\Rightarrow (x+y)=\pm (x-20)$

$\Rightarrow y=-20$ and $y+2x=20$

Plotting them on co-ordinate axes, we get a right angled triangle with base $=20$ units and height $=40$ units.

Area of the bounded region $=\frac{1}{2}\times 20\times 40=400$ sq. units.