if ax+by+c = 0,bx+cy+a = 0,cx+ay+b = 0 are concurrent lines then (a2/2bc) (b2/2ca) (c2/2ab)= - Maths - Straight Lines

Question

if ax+by+c = 0,bx+cy+a = 0,cx+ay+b = 0 are concurrent lines then
(a2/2bc) (b2/2ca) (c2/2ab)=?

Rahul Raj · Accepted Answer

Dear student

as the lines are concurrent

abcbcacab=0R1→R1+R2+R3a+b+ca+b+ca+b+cbcacab=0(a+b+c)111bcacab=0(a+b+c)(bc-a2-b2+ac+ab-c2)=0  (expanding determinant)-(a+b+c)(a2+b2+c2-ab-bc-ca)=0-(a+b+c)12(a-b)2+(b-c)2+(c-a)2=0so eithera+b+c=0or a=b=cgiven expression =a22bcb22cac22ab=a2b2c28a2b2c2=1/8if given expression = a22bc+b22ca+c22ab=12+12+12=32 for a=b=c

Regards

if ax+by+c = 0,bx+cy+a = 0,cx+ay+b = 0 are concurrent lines then (a2/2bc) (b2/2ca) (c2/2ab)=?

if ax+by+c = 0,bx+cy+a = 0,cx+ay+b = 0 are concurrent lines then (a²/2bc) (b²/2ca) (c²/2ab)=?