Home
Class 12
MATHS
If the curves x^(2)-y^(2)=4 and xy = sqr...

If the curves `x^(2)-y^(2)=4` and `xy = sqrt(5)` intersect at points A and B, then the possible number of points (s) C on the curve `x^(2)-y^(2) =4` such that triangle ABC is equilateral is

A

0

B

1

C

2

D

4

Text Solution

Verified by Experts

The correct Answer is:
A
A and B are `(sqrt(5),1)` and `(-sqrt(5),-1)`.
Let C be `(2 sec theta, 2 tan theta)`
`O(0,0)` is the mid point of Ab
Slope of `OC = sin theta` and slope of `AB = (1)/(sqrt(5))`
Since `OC _|_AB`
So, `sin theta =- sqrt(5)` which is impossible.
Promotional Banner

Similar Questions

Explore conceptually related problems

If curves (x^2)/(a^2)-(y^2)/(b^2)=1 and xy= c^2 intersect othrogonally , then

If alpha ,beta, gamma are the parameters of points A,B,C on the circle x^2+y^2=a^2 and if the triangle ABC is equilateral ,then

The total number of points on the curve x^2-4y^2=1 at which the tangents to the curve are parallel to the line x=2y is

At what points on the curve x^(2)+y^(2)-2x-4y+1=0, the tangents are parallel to the y-a is?

What are the points of intersection of the curve 4x^(2)-9y^(2)=1 with its conjugate axis ?

The points of intersection of the curves x^(2)-y^(2)=5 and |y|=(6)/(|x|)

Coordinates of points on curve 5x^(2) - 6xy +5y^(2) - 4 = 0 which are nearest to origin are

The parabola y^(2)=4x and the circle having its center at (6,5) intersect at right angle.Then find the possible points of intersection of these curves.