Consider the given equation. 2x2−10xy+2λy2+5x−16y−3=0 Compare the given equation with, ax2+2hxy+by2+2gx+2fy+c=0 On comparing, the value are a=2,b=2λ,h=−5 g=‌‌
5
2
,f=−8,c=−3 As the given equations represents a pair of straight lines therefore |
a
h
g
h
b
f
g
f
c
|=0 |
2
−5
5∕2
−5
2λ
−8
5∕2
−8
−3
|=0 2(−6λ−64)+5(15+20)+‌‌
5
2
(40−5λ)=0 λ=6 The point of intersection is (‌‌