Question

Area of the triangle formed by the line $4x+y=3$ and angles bisector of the pair of straight lines $x^2-y^2+2y=1$ is :

• A. $2$ sq. units
• B. $4$ sq. units
• C. $6$ sq. units
• D. $8$ sq. units

Answer 1

Answer: (A)

$2$ sq. units

General equation straight line is given by $A{x}^2+2Hxy+B{y}^2$

$\Rightarrow x^2-y^2+2y=1$

$\Rightarrow x=\pm (y-1)$

Bisector of above lines are so area between $x=0,y=1$ and $x+y=3$

$=\frac{1}{2}\times 2\times 2=2$ sq. units.