Prove that the lines `2x^2+6xy+y^2=0` are equally inclined to the lines `4x^2+18xy+y^2=0`

If the lines given by ax^(2)+2hxy+by^(2)=0 are equally inclined to the lines given by ax^(2)+2hxy+by^(2)+lambda(x^(2)+y^(2))=0 , then

Show that the pair of lines given by a^2x^2+2h(a+b)xy+b^2y^2=0 is equally inclined to the pair given by ax^2+2hxy+by=0 .

If the lines y=3x + 1 and 2y = x +3 are equally inclined to the line y= mx +4 , find the value of m.

The combined equation of the lines L_1 and L_2 is 2x^2+6xy+y^2=0 , and that of the lines L_3 and L_4 is 4x^2+18xy+y^2=0 . If the angle between L_1 and L_4 be alpha , then the angle between L_2 and L_3 will be .

Find the condition that one of the lines given by ax^2+2hxy+by^2=0 may coincide with one of the lines given by a' x^2 +2h'xy+b'y^2=0

Statement I . The combined equation of l_1,l_2 is 3x^2+6xy+2y^2=0 and that of m_1,m_2 is 5x^2+18xy+2y^2=0 . If angle between l_1,m_2 is theta , then angle between l_2,m_1 is theta . Statement II . If the pairs of lines l_1l_2=0,m_1 m_2=0 are equally inclined that angle between l_1 and m_2 = angle between l_2 and m_1 .

The lines represented by x^(2)+2lambda xy+2y^(2)=0 and the lines represented by (1+lambda)x^(2)-8xy+y^(2)=0 are equally inclined, then

Number of points lying on the line 7x+4y+2=0 which is equidistant from the lines 15x^2+56xy+48y^2=0 is

The distance of the point of intersection of the lines 2 x- 3y + 5 = 0 and 3x + 4y =0 from the line 5x-2y =0 is

Prove that The lines joining the origin to the points of intersection of the line 3x-2y =1 and the curve 3x^2 + 5xy -3y^2+2x +3y= 0 , are are at right angles.