are two perpendicular chords of the rectangular hyperbola xy=c2˙
is the center of the rectangular hyperbola, then find the value of product of the slopes of CP,CQ,CR,
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Two tangents to the hyperbola a2x2−b2y2=1
cut the axes at four concyclic points. Fid the value of m1m2˙
Find the asymptotes of the curve xy−3y−2x=0
A hyperbola passes through (2,3) and has asymptotes 3x−4y+5=0
. Then, the equation of its transverse axis is
Find the equation of tangents to the curve 4x2−9y2=1
which are parallel to 4y=5x+7.
Find the equation of the hyperbola which has 3x−4y+7=0
as its asymptotes and which passes through the origin.
An ellipse and a hyperbola are confocal (have the same focus) and the conjugate axis of the hyperbola is equal to the minor axis of the ellipse. If e1ande2
are the eccentricities of the ellipse and the hyperbola, respectively, then prove that e121+e221=2
Suppose the circle having equation x2+y2=3
intersects the rectangular hyperbola xy=1
at points A,B,C,andD˙
The equation x2+y2−3+λ(xy−1)=0,λ∈R,
a pair of lines through the origin for λ=−3
an ellipse through A,B,C,andD
a parabola through A,B,C,andD
a circle for any λ∈R
is the length of the latus rectum of the hyperbola for which x=3andy=2
are the equations of asymptotes and which passes through the point (4, 6), then the value of 2L