Consider a hyperbola xy=4 and a line y=2x=4. O is the centre of hyperbola. Tangent at any point P of hyperbola intersect the coordinate axes at A and B. Shortest distance between the line and hyperbola is
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If a hyperbola passing through the origin has 3x−4y−1=0
as its asymptotes, then find the equation of its transvers and conjugate axes.
The locus a point P(α,β) moving under the condition that the line y=αx+β is a tangent to the hyperbola a2x2−b2y2=1 is (A) a parabola (B) an ellipse (C) a hyperbola (D) a circle
Find the equation of hyperbola :
Whose foci are (4, 2) and (8, 2) and accentricity is 2.
Statement 1 : Every line which cuts the hyperbola 4x2−16y2=1 at
two distinct points has slope lying in (−2,2)˙
Statement 2 : The slope of the tangents of a hyperbola
lies in (−∞,−2)∪(2,∞)˙
The length of the transverse axis of the rectangular hyperbola xy=18
6 (b) 12 (c) 18 (d) 9
Find the eccentricity of the hyperbola given by equations x=2et+e−1andy=3et−e−1,t∈R˙
Each of the four inequalities given below defines a region in the xy plane. One of these four regions does nothave the following property. For any two points (x1,y2)and(y1,y2) in the region the piont (2x1+x2⋅2y1+y2) is also in the region. The inequality defining this region is
If SandS′ are the foci, C is the center, and P is a point on a rectangular hyperbola, show that SP×SprimeP=(CP)2˙