Home
Class 12
MATHS
The distance of the focus of x^(2)-y^(2)...

The distance of the focus of `x^(2)-y^(2) =4`, from the directrix, which is nearer to it, is

A

`2sqrt(2)`

B

`sqrt(2)`

C

`4sqrt(2)`

D

`8sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`x^(2) -y^(2) =4` is rectangular hyperbola.
`:. e = sqrt(2)`
Required distance `= ae - a//e = 2 sqrt(2) -2//sqrt(2) = sqrt(2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

The minimum distance of a point on the curve y=x^(2)-4 from the origin is

Find the coordinates of the focus , axis, the question of the directrix and latus rectum of the parabola y^(2)=8x .

Let S is the focus of the parabola y^2 = 4ax and X the foot of the directrix, PP' is a double ordinate of the curve and PX meets the curve again in Q. Prove that P'Q passes through focus.

The distance of two points P and Q on the parabola y^(2) = 4ax from the focus S are 3 and 12 respectively. The distance of the point of intersection of the tangents at P and Q from the focus S is

If the tangent at any point P to the parabola y^(2)=4ax meets the directrix at the point K , then the angle which KP subtends at its focus is-

Show that the difference of the distances from each focus of any point on the hyperbola 9x^2-16y^2=144 is equal to the length of the transverse axis.

In each of the following find the coordinates of the focus , axis of the parabola , the equation of the directrix and the length of the latus rectum. x^(2)=6y

In each of the following find the coordinates of the focus , axis of the parabola , the equation of the directrix and the length of the latus rectum. y^(2)=10x

In each of the following find the coordinates of the focus , axis of the parabola , the equation of the directrix and the length of the latus rectum. y^(2)=12x .

In each of the following find the coordinates of the focus , axis of the parabola , the equation of the directrix and the length of the latus rectum. y^(2)=-8x