Find the condition that the expressions `a x^2-b x y+c y^2a n da_1x^2+b_1x y+c_1y^2` may have factors `y-m xa n dm y-x ,` respectively.

Find the condition that the expressions ax^(2)-bxy+cy^(2) and a_(1)x^(2)+b_(1)xy+c_(1)y^(2) may have factors y-mx and my-x respectively.

Find the condition that the line A x+B y=1 may be normal to the curve a^(n-1)y=x^ndot

Find the condition that the line A x+B y=1 may be normal to the curve a^(n-1)y=x^ndot

Find the condition that the line A x+B y=1 may be normal to the curve a^(n-1)y=x^ndot

Find the condition that the line A x+B y=1 may be normal to the curve a^(n-1)y=x^ndot

Find the conditions that the straight lines y=m_1x+c_1, y=m_2x+c_2a n d\ y=m_3x+c_3 may meet in a point.

The condition that the line y=mx+c may be a tangent to (y^(2))/(a^(2))-x^(2)/b^(2)=1 is

The condition that the line y=mx+c may be a tangent to (y^(2))/(a^(2))-x^(2)/b^(2)=1 is

The condition that the line y = mx+c may be a tangent to the hyperbola x^(2) //a^(2) -y^(2)//b^(2) =1 is

Find the coordinates that the straight lines y=m_(1)x+c_(1),y=m_(2)x+c_(2) and y=m_(2)x+c_(3) may meet in a point.