0,ax^(2)+2^(2)hxy+by^(2)=0

The condition that the equation ax^(2) + 2hxy + by^(2) + 2gx + 2fy +c=0 can take the form ax^(2) - 2hxy + by^(2)=0 , when shifting the origi is

If the lines ax^(2) + 2hxy + by^(2)= 0 are equally inclined with the coordinate axes then

Show that the following pairs of lines are equally inclined to each other. a^(2)x^(2)+2h(a+b)xy+b^(2)y^(2)=0, ax^(2)+2hxy+by^(2)=0 (a+b ne 0)

The image of the pair of lines represented by ax^(2)+2hxy+by^(2)=0 by the line mirror y=0 is ax^(2)-2hxy-by^(2)=0bx^(2)-2hxy+ay^(2)=0bx^(2)+2hxy+ay^(2)=0ax^(2)-2hxy+by^(2)=0

The pair of lines a^(2)x^(2)+2h(a+b)xy+b^(2)y^(2)=0 and ax^(2)+2hxy+by^(2)=0 are

The lines joining the origin to the points of intersectio of the curves ax^(2)+2hxy+by^(2)+2gx=0 and ax^(2)+2hxy+by^(2)+2gx=0 are at right angles if