[" 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 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 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 common factors of the expressions a_(1)x^(2)+b_(1)x+c_(1)anda_(2)x^(2)+b_(2)x+c_(1) where c_(1)ne0 .

Find the condition for the two concentric ellipses a_(1)x^(2)+b_(1)y^(2)=1 and a_(2)x^(2)+b_(2)y^(2)=1 to intersect orthogonally.

Show that the condition that the curves ax^(2) + by^(2) = 1 and a_(1)x^(2) + b_(1)y^(2) = 1 should intersect orthogonally such that (1)/(a) - (1)/(b) = (1)/(a_(1)) - (1)/(b_(1)) .

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

Find the condition for two lines a_(1)x+b_(1)y+c_(1)=0 and a_(2)x+b_(2)y+c_(2)=0 to be (i) parallel (ii) perpendicular

Find the condition for two lines a_(1)x+b_(1)y+c_(1)=0 and a_(2)x+b_(2)y+c_(2)=0 to be (i) parallel (ii) perpendicular