Show that the area of the triangle formed by the straight lines
`y=m_(1)x+c_(1),y=m_(2)x+c_(2)andx=0" is "(1)/(2)((c_(1)-c_(2))^(2))/(|m_(1)-m_(2)|)`

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 .

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

If m_1 and m_2 are the roots of the equation x^2-a x-a-1=0 , then the area of the triangle formed by the three straight lines y=m_1x ,y=m_2x , and y=a(a!=-1) is

The area of the triangle formed by the lines y=a x ,x+y-a=0 and the y-axis is (a) 1/(2|1+a|) (b) 1/(|1+a|) (c) 1/2|a/(1+a)| (d) (a^2)/(2|1+a|)

Statement - I: Equation of bisectors of the angles between the liens x=0 and y=0 are y=+-x Statement - II : Equation of the bisectors of the angles between the lines a_(1)x+b_(1)y+c_(1)=0anda_(2)x+b_(2)y+c_(2)=0 are (a_(1)x+b_(1)y+c_(1))/(sqrt(a_(1)^(2)+b_(1)^(2)))=+-(a_(2)x+b_(2)y+c_(2))/(sqrt(a_(2)^(2)+b_(2)^(2))) (Provided a_(1)b_(2)nea_(2)b_(1)andc_(1),c_(2)gt0)

If m_(1),m_(2) be the roots of the equation x^(2)+(sqrt(3)+2)x+sqrt(3)-1 =0 , then the area of the triangle formed by the lines y = m_(1)x,y = m_(2)x and y = 2 is

Show that the equation of the straight line throught (alpha,beta) and through the point of intersection of the lines a_(1)x+b_(1)y+c_(1)=0 anda_(2)x+b_(2)y+c_(2)=0 is (a_(1)x+b_(1)y+c_(1))/(a_(1)alpha+b_(1)beta+c_(1))=(a_(2)x+b_(2)y+c_(2))/(a_(2)alpha+b_(2)beta+c_(2))

The area of the parallelogram formed by the lines y=m x ,y=x m+1,y=n x ,a n dy=n x+1 equals. (a) (|m+n|)/((m-n)^2) (b) 2/(|m+n|) 1/((|m+n|)) (d) 1/((|m-n|))

The straight lines represented by (y-mx)^(2)=a^(2)(1+m^(2))and(y-nx)^(2)=a^(2)(1+n^(2)) form a

If l_(1), m_(1), n_(1) and l_(2), m_(2), n_(2) are direction cosines of two mutually perpendicular straight lines, then prove that the direction cosines of the straight line which is perpendicular to both the given lines are pm (m_(1)n_(2)-m_(2)n_(1)), pm (n_(1)l_(2)-n_(2)l_(1)), pm (l_(1)m_(2)-l_(2)m_(1))