The area of the triangle formed by the lines `y=m_(1x)+c_1, y=m_2, x+c_2a n dx=0` is `1/2((c_1+c_2)^2)/(|m_1-m_2|)` b. `1/2((c_1-c_2)^2)/(|m_1+m_2|)` c. `1/2((c_1-c_2)^2)/(|m_1-m_2|)` d. `((c_1-c_2)^2)/(|m_1-m_2|)`

Show that the area of the triangle formed by the lines y=m_(1)x+c_(1),y=m_(2)x+c_(2) and and is 2|m_(1)-m_(2)|

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 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.

Supose directioncoisnes of two lines are given by u l+vm+wn=0 and al^2+bm^2+cn^2=0 where u,v,w,a,b,c are arbitrary constnts and l,m,n are directioncosines of the lines. For u=v=w=1 if (n_1 n_2)/(l_1 l_2)=((a+b)/(b+c)) then (A) (m_1m_2)/(l_1 l_2)=((b+c))/((c+a)) (B) (m_1m_2)/(l_1 l_2)=((c+a))/((b+c)) (C) (m_1m_2)/(l_1 l_2)=((a+b))/((c+a)) (D) (m_1m_2)/(l_1 l_2)=((c+a))/((a+b))

The area of an equilateral triangle inscribed in the circle x^(2)+y^(2)+2ax+2by+c=0 is (m)/(n)(a^(2)+b^(2)-c) then the value of (1)/(sqrt(3))m+n is

If three lines whose equations are y=m_(1)x+c_(1),y=m_(2)x+c_(2) and y=m_(3)x+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 direction ratios of the bisector of the angle between the lines whose direction cosines are l_1,m_1,n_1 and l_2,m_2,n_2 are (A) l_1+l_2,m_1+m_2+n_1+n_2 (B) l_1-l_2,m_1-m_2-n_1-n_2 (C) l_1m_2-l_2m_1,m_1n_2-m_2n_1,n_1l_2-n_2l_1 (D) l_1m_2+l_2m_1,m_1n_2+m_2n_1,n_1l_2+n_2l_1

Joint equation of lines passing through the origin, and parallel to the lines y-m_(1)x+c_(1) and y=m_(1)x+c_(2) , is