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 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 .

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

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.

(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 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 m in N and mgeq2, prove that: |1 1 1m_(C_1)m+1_(C_1)m+2_(C_1)m_(C_2)m+1_(C_2)m+2_(C_2)|=1

If a = x^(m + n) . Y^(l), b = x^(n + l). Y^(m) and c = x^(l + m) . Y^(n) , Prove that : a^(m-n) . b^(n - 1) . c^(l-m) = 1

The lines which intersect the skew lines y=m x ,z=c ; y=-m x ,z=-c and the x-axis lie on the surface: (a.) c z=m x y (b.) x y=c m z (c.) c y=m x z (d.) none of these

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

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