If a!=b!=c write the condition for which...

If `a!=b!=c` write the condition for which the equations `(b-c)x+(c-a)y+(a-b)=0\ a n d\ (b^3-c^3)x+(c^3-a^3)x=y+(c^3-b^3)=0` represent the same line.

A

`a =b`

B

`b =c`

C

`c =a`

D

`a +b +c =0`

Verified by Experts

The correct Answer is:

A, B, C, D

Similar Questions

Explore conceptually related problems

The equation (b-c)x+(c-a)y+(a-b)=0 and (b^3-c^3)x+(c^3-a^3)y+a^3-b^3=0 will represent the same line if

Prove that the lines (b-c)x+(c-a)y+(a-b)=0, (c-a)x+(a-b)y+(b-c)=0 and (a-b)x+(b-c)y+(c-a)=0 are concurrent.

To find the condition that the three straight lines A_(1)x+B_(1)y+C_(1)=0, A_(2)x+B_(2)y+C_(2)=0 and A_(3)x+B_(3)y+C_(3)=0 are concurrent.

Find the condition on a , b ,c ,d such that equations 2a x^3+bx^2+c x+d=0 and 2ax^2+3b x+4c=0 have a common root.

In a triangle A B C ,a=4,b=3,/_A=60^0 then c is root of the equation c^2-3c-7=0 (b) c^2+3c+7=0 (c) c^2-3c+7=0 (d) c^2+3c-7=0

Solve the system of the equations: a x+b y+c z=d , a^2x+b^2y+c^2z=d^2 , a^3x+b^3y+c^3z=d^3 .

If a+b+c=0 then check the nature of roots of the equation 4a x^2+3b x+2c=0 where a ,b ,c in Rdot

Show that the roots of the equation (a^(2)-bc)x^(2)+2(b^(2)-ac)x+c^(2)-ab=0 are equal if either b=0 or a^(3)+b^(3)+c^(3)-3acb=0

If a,b and c are the roots of the equation x^3+2x^2+1=0 , find |[a,b,c],[b,c,a],[c,a,b]| .