Posted by Nadine on Monday, December 14, 2009 at 9:03am.
What is the orthogonal trajectory of y^2  x^2 = C ??

Calculus  MathMate, Monday, December 14, 2009 at 10:00am
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.
Answer This Question
Related Questions
 Math  Mark each of the following True or False. ___ a. All vectors in an ...
 mathematics  find orthogonal trajectory of family of circles x^2+y^2+2fy+1=0.
 Math  The functional determinant of x, e^x, and e^x is equal to___ The ...
 calculus  two curves are orthogonal at a point of intersection of their ...
 Calculus  Orthogonal Trajectories  Find the orthogonal trajectories of the ...
 Math  Vectors  Prove that vector i,j and k are mutually orthogonal using the ...
 calculus  if the tangent of two intersecting circles, at their points of ...
 Linear Algebra, orthogonal  The vector v lies in the subspace of R^3 and is ...
 Calculus  Resolve u=[3,4,7] into two orthogonal vectors, one of which is ...
 Calculus  Resolve u=[3,4,7] into two orthogonal vectors, one of which is ...
More Related Questions