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Rectangular Hyperbola is considered one of the most asked concept.
36 Questions around this concept.
The point of intersection of the curves whose parametric equations are and
, is given by
and
are the eccentricities of the hyperbolas
and
, then
A circle cuts rectangular hyperbola xy = 1 in the points then
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The foci of the ellipse and the hyperbola
coincide, then the value of
is
The eccentricity of the hyperbola whose latus-rectum is 8 and conjugate axis is equal to half the distance between the foci, is
The equation of the hyperbola with vertices (3, 0) and (−3, 0) and semi latus rectum 4, is given by
A tangent drawn to the hyperbola at
forms a triangle of area
sq. units with coordinate axes. The eccentricity of the hyperbola is equal to:
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If is a double ordinate of hyperbola
such that
is an equilateral triangle,
being the centre of the hyperbola. Then the eccentricity e of the hyperbola satisfies
The equation of the hyperbola whose foci are and
and eccentricity
is given by
If a circle cuts a rectangular hyperbola and the parameters of these four points be
respectively. Then
Rectangular Hyperbola
If the length of the transverse axis and the conjugate axis are equal (i.e. a = b) then the hyperbola is known as rectangular hyperbola or equilateral hyperbola.
This is the general equation of a rectangular hyperbola.
Rectangular Hyperbola xy = c2
If we rotate the coordinate axes by 45o keeping the origin fixed, then the axes coincide with lines y = x and y = -x
For rectangular hyperbola, xy = c2
Vertices: A(c, c) and A’(-c, -c)
Transverse axis: x = y
Conjugate axis: x = -y
Foci: S and S'
Directrices: x + y = √2, x + y = - √2
Length of latusrectum = AA’ =
Properties of rectangular Hyperbola:
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