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Rectangular Hyperbola is considered one of the most asked concept.
44 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
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 PQ is a double ordinate of hyperbola
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.
So,
This is the general equation of a rectangular hyperbola.
Rectangular Hyperbola
If we rotate the coordinate axes by
Using rotation, the equation
For rectangular hyperbola, xy = c2
1. Vertices:
2. Transverse axis:
3. Conjugate axis:
4. Foci:
5. Directrices:
6. Length of latusrectum
Properties of rectangular Hyperbola:
(i) The parametric equation of the rectangular hyperbola
(ii) The equation of the tangent to the rectangular hyperbola
(iii) The equation of the tangent at
(iv) The equation of the normal at
(v) The equation of the normal at
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