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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.
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