Question:
What is the area of the triangle formed by the line $x + y = 3$ and angle bisectors of the pair of straight lines $x^2 – y^2 + 2y = 1$.
Well I really have no idea how to even start the question. Please help me by pointing me in the right direction! I tried to find the two equations from the pair of straight line equation given, but couldn't.
Best Answer
$$x^2 - y^2 + 2y = 1\iff x^2 = y^2 -2y+1 = (y-1)^2 \iff y-1 = \pm x \iff y = 1\pm x$$
Thus the two intersecting lines are given by $y = 1+x$ and $y = 1-x$. The point of intersection is given by $(0, 1)$. One bisector is the y-axis: the line $x=0$. The other bisector is given by $y = 1$.
Can you take it from here?