Homogenous Equation Homework Statement - a & h

[alijan kk]

Homework Statement

Let f(x,y)=0 ---------> 1
be any equation in the variables x and y. Equation (1) is called a homogeneous equation of degree n (a positive integer) if :
f(kx,ky)=kⁿf(x,y)
for some real number k.
for example in equation (5) below , if we replace x and y by kx and ky respectively, we have

k²(y²-(m₁m₂)xy+m₁m₂x²)=0
k²f(x,y)=0
Thus (5) is a homogeneous equation of degree 2.
A general second degree homogeneous equation can be written as:
ax²+2hxy+by²=0

Homework Equations

(y-m₁x)(y-m₂x)=0
y²-(m₁+m₂)xy+m₁m₂x²=0

The Attempt at a Solution

but what are "a" and "h" are equal to ? my book doesnot tell any thing about it ,, or are they obvious from the equations.

 

[Mark44]

Homework Statement

Let f(x,y)=0 ---------> 1
be any equation in the variables x and y. Equation (1) is called a homogeneous equation of degree n (a positive integer) if :
f(kx,ky)=kⁿf(x,y)
for some real number k.
for example in equation (5) below , if we replace x and y by kx and ky respectively, we have

k²(y²-(m₁m₂)xy+m₁m₂x²)=0
k²f(x,y)=0
Thus (5) is a homogeneous equation of degree 2.
A general second degree homogeneous equation can be written as:
ax²+2hxy+by²

This is not an equation -- there is no = symbol.

Homework Equations

(y-m₁x)(y-m₂x)=0
y²-(m₁+m₂)xy+m₁m₂x²=0

The Attempt at a Solution

but what are "a" and "h" are equal to ? my book doesnot tell any thing about it ,, or are they obvious from the equations.

They are just unspecified constants.
It's similar to the idea that a quadratic equation in one variable can be written as $ax^2 + bx + c = 0$. Here, a, b, and c are real constants. What makes it a quadratic equation isn't the constants -- it's the fact it's a polynomial with the highest power of the variable being 2

 

[alijan kk]

This is not an equation -- there is no = symbol.

They are just unspecified constants.
It's similar to the idea that a quadratic equation in one variable can be written as $ax^2 + bx + c = 0$. Here, a, b, and c are real constants. What makes it a quadratic equation isn't the constants -- it's the fact it's a polynomial with the highest power of the variable being 2

that was my typing mistake,, there is "=0"