class 11

Math

Co-ordinate Geometry

Hyperbola

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) $(6,52 )$

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

If a variable line has its intercepts on the coordinate axes $eande_{prime},$ where $2e ande_{prime}2$ are the eccentricities of a hyperbola and its conjugate hyperbola, then the line always touches the circle $x_{2}+y_{2}=r_{2},$ where $r=$ 1 (b) 2 (c) 3 (d) cannot be decided

The asymptote of the hyperbola $a_{2}x_{2} +b_{2}y_{2} =1$ form with ans tangen to the hyperbola triangle whose area is $a_{2}tanλ$ in magnitude then its eccentricity is: (a) $secλ$ (b) $cosecλ$ (c) $sec_{2}λ$ (d) $cosec_{2}λ$

Find the angle between the asymptotes of the hyperbola $16x_{2} −9y_{2} =1$ .

If a ray of light incident along the line $3x+(5−42 )y=15$ gets reflected from the hyperbola $16x_{2} −9y_{2} =1$ , then its reflected ray goes along the line. $x2 −y+5=0$ (b) $2 y−x+5=0$ $2 y−x−5=0$ (d) none of these

The length of the transverse axis of the rectangular hyperbola $xy=18$ is 6 (b) 12 (c) 18 (d) 9

If $PQ$ is a double ordinate of the hyperbola $a_{2}x_{2} −b_{2}y_{2} =1$ 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 $x_{2}−9y_{2}=9$ that are drawn from (3, 2).

Find the eccentricity of the hyperbola given by equations $x=2e_{t}+e_{−1} andy=3e_{t}−e_{−1} ,t∈R˙$