Invariance

Question 1

Remember what does invariance mean

Answer 1

It means that after applied transformation Nothing changed

Question 2

What is the way to find invariant limes and invariant point of lines

Answer 2

Invariant point means xy translated to xy, so first way

Invariant LINE just means xy translated to another point on the line mx +c

Question 3

If you want invariant lines THROUGH THE ORIGIN what to do

Answer 3

Left side of the m2 thing set to 0. Whatever value that gives , if it doesn’t match right side then c must be 0 so these are your points where invariant lines are through the origin !

If you don’t want any chance of lines going through origin, there must be no solution Tom, so set discrimination to less than 0, will give you range for where there is no invariant