If `u=a_1x+b_1y+c_1=0,v=a_2x+b_2y+c_2=0,` and `(a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2),` then the curve `u+k v=0` is (a)the same straight line `u` (b)different straight line (c)not a straight line (d)none of these

For two linear equations , a_1x + b_1y + c_1=0 and a_2x + b_2y + c_2 = 0 , the condition (a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2) is for.

If a_1x+b_1y+c_1z=0, a_2x+b_2y+c_2z=0, a_3x+b_3y+c_3z=0 and |(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)|=0 , then the given system then

If the equations 4x + 6y = 15 and 8x +ky = 30 have infinite solutions, then find the value of k . The following are the steps involved in solving the above problem. Arrange them in sequential order. (A) (4)/(8) = (6)/(k) = (-15)/(-30) rArr (6)/(k) = (1)/(2) (B) We know that, if a_1x+ b_1y + c_1 =0 and a_2 x + b_2 y + c_2=0 have infinite solutions, then (a_1)/(a_2) = (b_1)/(b_2) = (c_1)/(c_2) . (C) Given that, 4x + 6y - 15 =0 and 8x + ky - 30 =0 have infinite solutions. (D) therefore k = 12 .

If (a_1)/(a_2) = (b_1)/(b_2) ne (c_1)/(c_2) , then the equations a_1x + b_1y + c_1 =0 and a_2x + b_2y + c_2=0 are _________. (consistent/inconsistent)

Let 2a+2b+c=0 , then the equation of the straight line ax + by + c = 0 which is farthest the point (1,1) is

If the line ((x)/(a))+((y)/(b))=1 moves in such a way that ((1)/(a^(2)))+((1)/(b^(2)))=((1)/(c^(2))), where c is a constant,prove that the foot of the perpendicular from the origin on the straight line describes the circle x^(2)+y^(2)=c^(2)

If {:A=[(n,0,0),(0,n,0),(0,0,n)]and B=[(a_1,a_2,a_3),(b_1,b_2,b_3),(c_1,c_2,c_3)]:} , then AB is equal to