Rectangular hyperbola:

The equation of rectangular hyperbola referred to its transverse and conjugate axes as coordinate axes is thus x² - y² = a².

Illustration : If tangent and normal to a rectangular hyperbola cut off intercepts a₁ and a₂ on one axis, and b₁ and b₂ on the other, show that a₁a₂ + b₁b₂ = 0.

Solution: Let rectangular hyperbola be x² - y² = a² and let (asecΦ, a tanΦ) be any point on this hyperbola. The equations of t angents and normals at this point are

                                          x secΦ, a tanΦ = a                          .....(i)

                              and xcosΦ + ycotΦ = 2a                  ...(ii)

                              as (i) and (ii) cut intercepts a₁, a₂ on x-axis, then

The equation of rectangular hyperbola with asymptotes as coordinate axes:

When the centre of any rectangular hyperbola be at the origin and its asymptotes concide with the coordinates axes, its equation is xy = c².

Illustration: If the normal at point 't₁' to the rectangular hyperbola xy = c² meets it again at point 't₂', prove that t₁³ = -1

Solution:  ince the equation of normal at  to the hyperbola xy = c² is   but this passes through  then

Email based Rectangular hyperbola Assignment Help -Rectangular hyperbola Homework Help

We at www.expertsmind.com offer email based Rectangular hyperbola assignment help - homework help and projects assistance from k-12 school level to university and college level and engineering and management studies. We provide finest service of Mathematics assignment help and Mathematic homework help. Our experts are helping students in their studies and they offer instantaneous tutoring assistance giving their best practiced knowledge and spreading their world class education services through e-Learning program.

Expertsmind's best education services

• Quality assignment-homework help assistance 24x7 hrs
• Best qualified tutor's network
• Time on delivery
• Quality assurance before delivery
• 100% originality and fresh work