How do I craft a linear equation so that it

Kris Patton

Kris Patton

Answered question

2022-02-22

How do I craft a linear equation so that it is in the form of ax+bx+c=0 where a2+b2=1 if I have two points? I know how to get it into the form ax+bx+c=0 but I can't figure out the algorithm for satisfying the second condition.

Answer & Explanation

Arif Coates

Arif Coates

Beginner2022-02-23Added 6 answers

I'm assuming you meant ax+by+c=0 so that this equation is that of a line.
If you have ax+by+c=0, then calculate m=a2+b2. Then dividing by m,amx+bmy+cm=0 satisfies the condition.
Kwame Malone

Kwame Malone

Beginner2022-02-24Added 5 answers

Starting from a linear equation jx+k=0, dividing by k we get jkx+1=mx+1=0. Now we have to solve the system formed by the equations a+b=m and a2+b2=1. This leads to a2am+m2212=0. The equation has real solutions for 2m20, i.e., m ranging between 2 and 2. In this case, a=m2±2m22 and b=m2±2m22.

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