Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
In a hyperbola b2 = a2 (e2 – 1). In the case of rectangular hyperbola (i.e., when b = a) result becomes a2 = a2(e2 – 1) or e2 = 2 or e = √2
i.e. the eccentricity of a rectangular hyperbola = √2.
In case of rectangular hyperbola a = b i.e., the length of transverse axis = length of conjugate axis.
A rectangular hyperbola is also known as an equilateral hyperbola.
The asymptotes of rectangular hyperbola are y = ± x.
If the axes of the hyperbola are rotated by an angle of -π/4 about the same origin, then the equation of the rectangular hyperbola x2 – y2 = a2 is reduced to xy = a2/2 or xy = c2.
When xy = c2, the asymptotes are the coordinate axis.
Length of latus rectum of rectangular hyperbola is the same as the transverse or conjugate axis.
Rectangular Hyperbola with asymptotes as coordinate axis:
The equation of the hyperbola which has its asymptotes as the coordinate axis is xy = c2 with parametric representation x = ct and y = c/t, t ∈ R-{0}.
The equations of the directrices of the hyperbola in this case are x + y = ± √2c.
Since, the transverse and the conjugate axes are the same hence, length of latus rectum = 2√2c = T.A. = C.A.
Equation of a chord whose middle point is given to be (p, q) is qx + py = 2pq.
The equation of the tangent at the point P(x1, y1) is x/x1 + y/y1 = 2 and at P(t) is x/t + ty = 2c.
Equation of normal is y-c/t = t2(x-ct).
The equation of the chord joining the points P(t1) and Q(t2) is x + t1t2y = c(t1 + t2) and its slope is m = -1/t1t2.
The vertices of the hyperbola are (c, c) and (-c, -c) and the focus is (√2c, √2c) and (-√2c, -√2c).
Get your questions answered by the expert for free
You will get reply from our expert in sometime.
We will notify you when Our expert answers your question. To View your Question
Win Gift vouchers upto Rs 500/-
Register Yourself for a FREE Demo Class by Top IITians & Medical Experts Today !