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

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.

Find the coordinates that the straight lines y=m_(1)x+c_(1),y=m_(2)x+c_(2) and y=m_(2)x+c_(3) may meet in a point.

The condition that the lines y=m_(1)x+c_(1), y=m_(2)x+c_(2), y=m_(3)x+c_(3) are concurrent is

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

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

(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

(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

Show that the area of the triangle formed by the straight lines y = m_(1) x + c_(1) , y = m_(2) x + c_(2) and x = 0 is (1)/(2)(c_(1)-c_(2))^(2)/(|m_(1)-m_(2)|) sq . Units .

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 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_2)+m_3(c_1-c_2) = 0