Eq. of AC AC=(cos‌α−sin‌α)+(sin‌α+cos‌α)y=10 BD=(sin‌α−cos‌α)x+(sin‌α−cos‌α)y=0 (10(cos‌α−sin‌α),10(sin‌α−cos‌α)) Slope of AC=(‌
sin‌α−cos‌α
sin‌α+cos‌α
)=tan‌θ=M Eq. of line making an angle π4 with AC m1,m2=‌
m±tan‌
Ï€
4
1±m‌tan‌
Ï€
4
=‌
m+1
1−m
or ‌
m−1
1+m
‌
‌
sin‌α−cos‌α
sin‌α+cos‌α
+1
1−(‌
sin‌α−cos‌α
sin‌α+cos‌α
)
,‌
‌
sin‌α−cos‌α
sin‌α+cos‌α
−1
1+‌
sin‌α−cos‌α
sin‌α+cos‌α
m1,m2=tan‌α,cot‌α mid point of AC&‌BD =M(5(cos‌α−sin‌α),5(cos‌α+sin‌α)) B (10(cos‌α−sin‌α),10(cos‌α+sin‌α)) a=AB=√2‌BM=√2(5√2)=10 a=10 ∵a2+11a+3(m12+‌