If the equations `ax^2 + 2hxy+by^2 =0 and y^2 - (m_1 + m_2) xy+m_1 m_2 x^2 =0` represent the same curve, find `m_1 +m_2 and m_1 m_2`.

If the equation ax^(2)+2hxy+by^(2)=0 represented two lines y=m_(1)x and y=m_(2)x the

If m in Z and the equation m x^(2) + (2m - 1) x + (m - 2) = 0 has rational roots, then m is of the form

If the equation m^(2)(x + 1) + m(y – 2) + 1 = 0 represents a family of lines, where ‘m’ is parameter then find the equation of the curve to which these lines will always be tangents.

If (m-2,2m+1) lies on equation 2x+3y-10=0 find m

If the equation ax^(2)-6xy+y^(2)=0 represents a pair of lines whose slopes are m and m^(2), then the value(s) of a is/are

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 inclinded that angle between l_1 and m_2 = angle between l_2 and m_1 .

31. If the lines represented byax? + 2hxy + by2 + 2gx + 2 fy+c= 0 are writtenin the form y=mx+c1 and y = m2x+C2,then1) m + m2 = alb, mm2 = 2h1b2) m + m2 =-2h/b, mm2 = alb3) m, + m2 = -2h/b, m,m, = -b/a4) m, + m2 = 2h/b, m,m, = a / b

(i) Find the value of 'a' if the lines 3x-2y+8=0 , 2x+y+3=0 and ax+3y+11=0 are concurrent. (ii) If the lines y=m_(1)x+c_(1) , y=m_(2)x+c_(2) and y=m_(3)x+c_(3) meet at point then shown that : c_(1)(m_(2)-m_(3))+c_(2)(m_(3)-m_(1))+c_(3)(m_(1)-m_(2))=0