The lines `a^2x^2+bcy^2=a(b+c)xy` will be coincident , if

Options

A. `a=0 or b=c`
B. `a=b or a=c`
C. `c=0 or a =b `
D. `a=b+c`

Answer

A

Explanation

Given , `a^2x^2+bcy^2=a(b+c)xya^2x^2+bcy^2-a(b+c)xy=0`
On comparing it with homogenous equation of second degree , we have

`A=a^2,B=bc, H=(-a(b+c))/(4)`
Since , lines are coincident ,
`therefore H^2-AB=0rArr=(a^2(b+c)^2)/(4)-a^2bc=0`
`rArr (a^2(b^2+c^2+2abc))/(4)-a^2bc=0`
`rArr (a^2b^2+a^2c^2+2a^2bc-4a^2bc)/(4)=0`
`rArr (a^2(b^2+c^2-2bc))/(4)=0`
`rArr a(b-c)=0`
`rArr a=0 or b-c=0`
`therefore a=0 or b=c`