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

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 has, 1) more than two solutions 2) one trivial and one non trivial solutions 3) no solution 4) only trivial solution (0, 0, 0)

If a_1x^2 + b_1 x + c_1 = 0 and a_2x^2 + b_2 x + c_2 = 0 has a common root, then the common root is

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^2dot

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^2dot

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^2dot

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^2dot

(1) The straight lines (2k+3) x + (2-k) y+3=0 , where k is a variable, pass through the fixed point (-3/7, -6/7) . (2) The family of lines a_1 x+ b_1 y+ c_1 + k (a_2 x + b_2 y + c_2) = 0 , where k is a variable, passes through the point of intersection of lines a_1 x + b_1 y + c_1 = 0 and a_2 x+ b_2 y + c_2 = 0 (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not a correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

If b_1. b_2=2(c_1+c_2) then at least one of the equation x^2+b_1x+c_1=0 and x^2+b_2x+c_2=0 has a) imaginary roots b) real roots c) purely imaginary roots d) none of these

Show that two lines a_1x+b_1y+c_1=0 and a_2x+b_2y+c_2=0 , where b_1,b_2!=0 are : (i) Parallel if (a_1)/(b_1)=(a_2)/(b_2), and (ii) perpendicular if a_1a_2+b_1b_2=0 .