Second degree homogeneous equation in x and y always represents

State (with reasons), which of the following are true or false : Every second degree equation in x and y represents a circle.

A graph of linear equation always represents a :

An express way is represented by equation x-y=0 and a highway is represented by equation x-y=-2 . Represent this situation geometrically.

A polynomial equation in x of degree n always has :

Show that a homogeneous equations of degree two in x and y , i.e., ax^(2) + 2 hxy + by^(2) = 0 represents a pair of lines passing through the origin if h^(2) - 2ab ge 0 .

Order and degree of differential equation are always Positive integers

Order and degree of differential equation are always …………integers