Asked by Nadine
What is the orthogonal trajectory of y^2 - x^2 = C ??
Answers
Answered by
MathMate
Using implicit differentiation, find the slope of the tangents
y'=x/y
The slopes of the normals are therefore:
y'=-y/x
Rearrange and integrate
∫y'/y = ∫-1/x
ln y = -ln x + C1
ln y = -k ln x
raise to the power of e:
y=C/x
This is the family of reciprocal curves, or rectangular hyperbolas.
y'=x/y
The slopes of the normals are therefore:
y'=-y/x
Rearrange and integrate
∫y'/y = ∫-1/x
ln y = -ln x + C1
ln y = -k ln x
raise to the power of e:
y=C/x
This is the family of reciprocal curves, or rectangular hyperbolas.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.