Divisors satisfying specific condition

Find the equation of the family of lines satisfying the following condition : passing through the origin .

Find the equation of the family of lines satisfying the following condition : having slope 5.

Find the quation of the parabolas with vertices at the origin and satisfying the following conditions. Focus at (0,-a)

Find the quation of the parabolas with vertices at the origin and satisfying the following conditions. Focus at (a,0)

Find the quation of the parabolas with vertices at the origin and satisfying the following conditions. Focus at (0,a)

Find the equations of the parabola with vertices at the origin and satisfying the following condition : Focus at (- a, 0).