If the straight lines ax + by + P = 0 and $\mathbf{x}\mathbf{cos}\mathbf{\alpha }\mathbf{+}\mathbf{y}\mathbf{sin\alpha }\mathbf{-}\mathbf{P}\mathbf{=}\mathbf{0}$ include an angle $\mathbf{\pi }\mathbf{/}\mathbf{4}$  between them and meet the straight line $\mathbf{x}\mathbf{sin}\mathbf{\alpha }\mathbf{-}\mathbf{ycos\alpha }\mathbf{=}\mathbf{0}$  in the same point, then the value of $a^2 + b^2 =$ ______

Give that ax + by + P = 0 &  $\text{x\hspace{0.17em}cos\hspace{0.17em}α+y\hspace{0.17em}sinα\hspace{0.17em}=\hspace{0.17em}P}$
Are inclined at an angle  $\text{π/4}$
i.e.,  $\text{tan\hspace{0.17em}}\frac{\text{π}}{\text{4}}\text{\hspace{0.17em}=\hspace{0.17em}}\frac{\text{-}\frac{\text{a}}{\text{b}}\text{+}\frac{\text{cosα}}{\text{sinα}}}{\text{1+}\frac{\text{a\hspace{0.17em}cosα}}{\text{bsin\hspace{0.17em}α}}}$
$\text{a\hspace{0.17em}cos\hspace{0.17em}α\hspace{0.17em}+\hspace{0.17em}b\hspace{0.17em}sin\hspace{0.17em}α\hspace{0.17em}=\hspace{0.17em}-\hspace{0.17em}a\hspace{0.17em}sin\hspace{0.17em}α\hspace{0.17em}+\hspace{0.17em}b\hspace{0.17em}cos\hspace{0.17em}}\alpha \stackrel{ }{\to }\left(1\right)$  
And also given ax + by + P = 0, $\text{x\hspace{0.17em}cos\hspace{0.17em}α\hspace{0.17em}+\hspace{0.17em}y\hspace{0.17em}sin\hspace{0.17em}α-P=0}$ ,
 $\text{x\hspace{0.17em}sin\hspace{0.17em}α\hspace{0.17em}-\hspace{0.17em}y\hspace{0.17em}cos\hspace{0.17em}α\hspace{0.17em}= 0}$ are concurrent
We get a $\text{cos\hspace{0.17em}α\hspace{0.17em}+\hspace{0.17em}b\hspace{0.17em}sinα\hspace{0.17em}=\hspace{0.17em}-1}\stackrel{ }{\to }\left(\text{2}\right)$
From (1) and (2) , we get
 $\text{-\hspace{0.17em}a\hspace{0.17em}sin\hspace{0.17em}α\hspace{0.17em}+\hspace{0.17em}b\hspace{0.17em}cos\hspace{0.17em}α\hspace{0.17em}=\hspace{0.17em}-1}\stackrel{ }{\to }\left(\text{3}\right)$
From (2) & (3) , we get
a2 + b2 = 2