If the vertices of the hyperbola be at (−2,0) and (2,0) and one of the foci be at (−3,0) then which one of the following points does not lie on the hyperbola? (a) (−6,210) (b) (26,5) (c) (4,15) (d) (6,52)
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If a variable line has its intercepts on the coordinate axes eandeprime,
are the eccentricities of a hyperbola and its conjugate hyperbola, then the line always touches the circle x2+y2=r2,
1 (b) 2 (c) 3 (d) cannot be decided
The asymptote of the hyperbola a2x2+b2y2=1 form with ans tangen to the hyperbola triangle whose area is a2tanλ in magnitude then its eccentricity is: (a) secλ (b) cosecλ (c) sec2λ (d) cosec2λ
Find the angle between the asymptotes of the hyperbola 16x2−9y2=1
If a ray of light incident along the line 3x+(5−42)y=15
gets reflected from the hyperbola 16x2−9y2=1
, then its reflected ray goes along the line.
(d) none of these
The length of the transverse axis of the rectangular hyperbola xy=18
6 (b) 12 (c) 18 (d) 9
is a double ordinate of the hyperbola a2x2−b2y2=1
such that OPQ
is an equilateral triangle, O
being the center of the hyperbola, then find the range of the eccentricity e
of the hyperbola.
Find the equations of the tangents to the hyperbola x2−9y2=9
that are drawn from (3, 2).
Find the eccentricity of the hyperbola given by equations x=2et+e−1andy=3et−e−1,t∈R˙