Help on Ellipse Example 5.4L - Understand m1 & m2

[Michael_Light]

I need help with example 5.4L. I can understand all the working steps but i don't understand how they get m₁ and m₂, which is the point of intersection of the two perpendicular tangent... Can anyone enlighten me?

 

[I like Serena]

View attachment 33287


I need help with example 5.4L. I can understand all the working steps but i don't understand how they get m₁ and m₂, which is the point of intersection of the two perpendicular tangent... Can anyone enlighten me?

First they determine what the equation is for a tangent for any given slope m.

Since they want to find the intersection of two tangents that are perpendicular to each other, they start with two tangents that have arbitrary slopes m1 and m2.

Then they introduce the condition that they are perpendicular.

And they solve the equations to find to point of intersection.