Home
Class 12
MATHS
If two tangents can be drawn the differe...

If two tangents can be drawn the different branches of hyperbola `(x^(2))/(1)-(y^(2))/(4) =1` from `(alpha, alpha^(2))`, then

A

`alpha in (-2,0)`

B

`alpha in (0,2)`

C

`alpha in (-oo,-2)`

D

`alpha in(2,oo)`

Text Solution

Verified by Experts

The correct Answer is:
C, D
`(alpha, alpha)^(2)` must lie between the asymptotes of hyperbola `(x^(2))/(1)-(y^(2))/(4) =1` in I and II quadrant. Asymptotes are `y = +- 2x rArr 2alpha lt alpha^(2) rArr alpha 0` or `alpha gt 2`. and `-2alpha lt alpha^(2) rArr alpha lt -2` or `alpha gt 0 rArr alpha in (-oo,-2) uu(2,oo)`
Promotional Banner

Similar Questions

Explore conceptually related problems

If two distinct tangents can be drawn from the point (alpha, alpha+1) on different branches of the hyperbola (x^(2))/(9)-(y^(2))/(16)=1 , then find the values of alpha .

If two distinct tangents can be drawn from the Point (alpha,2) on different branches of the hyperbola x^2/9-y^2/(16)=1 then (1) |alpha| lt 3/2 (2) |alpha| gt 2/3 (3) |alpha| gt 3 (4) alpha =1

The points on the ellipse (x^(2))/(2)+(y^(2))/(10)=1 from which perpendicular tangents can be drawn to the hyperbola (x^(2))/(5)-(y^(2))/(1) =1 is/are

Tangents drawn from the point (c, d) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 make angles alpha and beta with the x-axis. If tan alpha tan beta=1 , then find the value of c^(2)-d^(2) .

How many real tangents can be drawn from the point (4, 3) to the hyperbola (x^2)/(16)-(y^2)/9=1? Find the equation of these tangents and the angle between them.

If the chords of contact of tangents from two points (-4,2) and (2,1) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are at right angle, then find then find the eccentricity of the hyperbola.

Find the equation of pair of tangents drawn from point (4, 3) to the hyperbola (x^(2))/(16)-(y^(2))/(9)=1 . Also, find the angle between the tangents.

Two tangents are drawn from a point on hyperbola x^(2)-y^(2)=5 to the ellipse (x^(2))/(9)+(y^(2))/(4)=1 . If they make angle alpha and beta with x-axis, then

If tangents drawn from the point (a ,2) to the hyperbola (x^2)/(16)-(y^2)/9=1 are perpendicular, then the value of a^2 is _____

Statement 1 : If from any point P(x_1, y_1) on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 , tangents are drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1, then the corresponding chord of contact lies on an other branch of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 Statement 2 : From any point outside the hyperbola, two tangents can be drawn to the hyperbola.