If the line `a_1 x + b_1 y+ c_1 = 0 and a_2 x + b_2 y + c_2 = 0` cut the coordinate axes in concyclic points, prove that : `a_1 a_2 = b_1 b_2`.

If the origin lies in the acute angle between the lines a_1 x + b_1 y + c_1 = 0 and a_2 x + b_2 y + c_2 = 0 , then show that (a_1 a_2 + b_1 b_2) c_1 c_2 lt0 .

(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

(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

Show that two lines a_(1) x + b_(14) y + c_(1) = 0 and a_(2) x + b_(2) y + c_(2) = 0 , where b_(1) , b_(2) ne 0 are (i) Parallel if (a_1)/( b_1) = (a_2)/( b_2) and

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 curves a_1 x^2 + 2h_1 xy + b_1 y^2 - 2g_1 x - 2f_y y + c = 0 and a_2 x^2 - 2h_2xy + (a_2 + a_1 - b_1) y^2 - 2g_2 x - 2f_2 y + c = 0 intersect in four concyclic points A, B, C and D . and H be the point ((g_1+g_2)/(a_1 + a_2), (f_1 + f_2)/(a_1 + a_2)) , then (5HA^2 + 7HB^2 + 8HC^2)/(HD^2) = ..

In the pair of linear equations a_1x+b_1y+c_1=0 and a_2x+ b_2y + C_2 = 0. If a_1/a_2 ne b_1/b_2 then the

If the lines drawn to the linear equations of the type a_1 x+b_1 y+c_1=0 and a_2 x+b_2 y+c_2 =0 are coincident on each other, then the correct relation among the following is

Show that two lines a_1 x+b_1 y+c_1=0 and a_2 x+b_2 y+c_2=0 . where b_1, b_2 ne 0 are: (i) Parallel if a_1/b_1=a_2/b_2 , and (ii) Perpendicular if a_1 a_2+b_1 b_2=0

Find the condition so that the two equations a_1 x^2+b_1 x+c_1=0 and a_2 x^2+b_2 x+c_2=0 will have a common root.