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`.

8.If the lines a_(1)x+b_(1)y+c_(1)=0 and a_(2)x+b_(2)y+c_(2)=0 cuts the coordinate axes in concyclic points then

If the lines a_(1)x+b_(1)y+c_(1)=0 and a_(2)x+b_(2)y+c_(2)=0 cut the coordinae axes at concyclic points,then prove that |a_(1)a_(2)|=|b_(1)b_(2)|

(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

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.

Statement-1: If the equations ax^2 + bx + c = 0 (a, b, c in R and a != 0) and 2x^2 + 7x+10=0 have a common root, then (2a+c)/b =2. Statement-2: If both roots of a_1 x^2 + b_1 x+c_1 = 0 and a_2 x^2 + b_2x + c_2 = 0 are same, then a_1/a_2=b_1/b_2=c_1/c_2. Given a_1,b_1,c_1,a_2,b_2,c_2 in R and a_1 a_2 != 0. (i) Statement I is true , Statement II is also true and Statement II is correct explanation of Statement I (ii)Statement I is true , Statement II is also true and Statement II is not correct explanation of Statement I (iii) Statement I is true , Statement II is False (iv) Statement I is False, Statement II is True

In direct proportion a_1/b_1 = a_2/b_2

If 1, a_1,a_2,a_3 ,…, a_(n-1) are the nth roots of unity then prove that : 1+a_1+a_2+…+a_(n-1) =0.

If the tangent and normal to xy=c^2 at a given point on it cut off intercepts a_1, a_2 on one axis and b_1, b_2 on the other axis, then a_1 a_2 + b_1 b_2 = (A) -1 (B) 1 (C) 0 (D) a_1 a_2 b_1 b_2