Show that the lines `y-m_1 x-c_1 = 0`, `y-m_2x-c_2 = 0 `and `y-m_3 x-c_3 =0` form an isosceles triangle with the first line as base if : `(1+m_1 m_2) (m_1 - m_3) + (1+m_1 m_3) (m_1 - m_2) = 0`

If the lines whose equations are y=m_1 x+ c_1 , y = m_2 x + c_2 and y=m_3 x + c_3 meet in a point, then prove that : m_1 (c_2 - c_3) + m_2 (c_3 - c_1) + m_3 (c_1 - c_2) =0

Find the conditions that the straight lines y=m_1x+c_1, y=m_2x+c_2a n d\ y=m_3x+c_3 may meet in a point.

The area of the triangle whose sides y=m_1 x + c_1 , y = m_2 x + c_2 and x=0 is

The line l_1 x+ m_1 y+n=0 and l_2 x + m_2 y+n=0 will cut the coordinate axes at concyclic points if (A) l_1 m_1 = l_2 m_2 (B) l_1 m_2 = l_2 m_1 (C) l_1 l_2 = m_1 m_2 (D) l_1 l_2 m_1 m_2 = n^2

(i) Find the value of 'a' if the lines 3x-2y+8=0 , 2x+y+3=0 and ax+3y+11=0 are concurrent. (ii) If the lines y=m_(1)x+c_(1) , y=m_(2)x+c_(2) and y=m_(3)x+c_(3) meet at point then shown that : c_(1)(m_(2)-m_(3))+c_(2)(m_(3)-m_(1))+c_(3)(m_(1)-m_(2))=0

If y=m_1x+c and y=m_2x+c are two tangents to the parabola y^2+4a(x+a)=0 , then (a) m_1+m_2=0 (b) 1+m_1+m_2=0 (c) m_1m_2-1=0 (d) 1+m_1m_2=0

The lines y=m_1x ,y=m_2xa n dy=m_3x make equal intercepts on the line x+y=1. Then (a) 2(1+m_1)(1+m_3)=(1+m_2)(2+m_1+m_3) (b) (1+m_1)(1+m_3)=(1+m_2)(1+m_1+m_3) (c) (1+m_1)(1+m_2)=(1+m_3)(2+m_1+m_3) (d) 2(1+m_1)(1+m_3)=(1+m_2)(1+m_1+m_3)

If three lines whose equations are y=m_1x+c_1,y=m_2x+c_2 and y=m_3x+c_3 are concurrent, then show that m_1(c_2-c_3)+m_2(c_3-c_1)+m_3(c_1-c_2)=0 .

If y=m_1x+c and y=m_2x+c are two tangents to the parabola y^2+4a(x+c)=0 , then m_1+m_2=0 (b) 1+m_1+m_2=0 m_1m_2-1=0 (d) 1+m_1m_2=0

The line y=mx+1 is a tangent to the parabola y^2 = 4x if (A) m=1 (B) m=2 (C) m=4 (D) m=3