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) + ( sqrt(3) + 2) x + sqrt(3) - 1 =0 then prove that area of the triangle formed by the lines y=m_(1) x, y=m_(2) x and y=c is (c^2)/( 4) ( sqrt(33) + sqrt(11)) .

Using integration , find the area of triangular region formed by the lines x+2y =2 , y-x=1 and 2x +y=7

Find the area of the triangle formed by the lines represented by ax^2+2hxy+by^2+2gx+2fy+c=0 and axis of x .

Compute the area bounded by the lines x+ 2y = 2 , y - x=1 and 2x +y =7

Obtain the area of equilateral triangle inscribed in circle x^(2) + y^(2) + 2gx + 2fy + c = 0 .

Find the area of the parallelogram formed by the lines 2x^2+5xy+3y^2=0 and 2x^2+5xy+3y^2+3x+4y+1=0

Find the area of the region bounded by the parabola y=x^2 +1 and the lines y=x ,x=0 and x=2.

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 .

Find the angle between the lines l_(1) : y= (2 - sqrt(3) ) ( x +5) and l_(2) : y=(2+ sqrt(3) ) ( x-7) . Thinking Process : If the angle between the lines having the slope m_1 and m_2 is theta then tan theta = | ( m_1 - m_2)/( 1+ m_1 m_2) | . Use this formula to solve the above problem.

The area of region bounded by the curve y= x-x^2 and line y= mx is 9/2 then the value of m is ……..