Prove that the triangle formed by the lines `ax^2+2hxy+by^2=0 and lx+my=1 ` isosceles, if `h(l^2-m^2)=(a-b)lm `.

Area of the triangle formed by the lines y^2-9xy+18x^2=0 and y=9 is

Show that the area of the triangle formed by the lines ax^2+2hxy+by^2=0 and lx+my+n=0 is (n^2sqrt((h^2-ab)))/(|(am^2-2hlm+bl^2)|)

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 .

The lines (lx+my)^2-3(mx-ly)^2=0 and lx+my+n=0 forms

Show that the centroid (x',y') of the triangle with sides ax^2+2hxy+by^2=0 and lx +my =1 , is given by (x')/(bl-hm)=(y')/(am-hl)=(2)/(3(am^2-2hlm+bl^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)) .

if h^2=ab , then the lines represented by ax^2+2hxy+by^2=0 are

The lines y = mx bisects the angle between the lines ax^(2) +2hxy +by^(2) = 0 if

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 | ) .

Find the centroid of the triangle formed by the line 2x + 3y - 6 = 0, with the coordinate axes.