00:01
Hello everyone in this problem we are given with the three points the points are minus 0 .1 0 .3 0 .2 and 0 .1 .1 now for these points we need to find the hyperbolic distance for the each pair of points and we need to compare the obtained hyperbolic distance with the corresponding uclean distances so the hyperbolic distance formula for the points x1 y1 and x2 y2 will be given as d1 dash which is equal to cos h inverse of cos h of y 1 cos h of x2 minus x1 into cos h of y2 minus sine h of y1 times of sine h of y2.
01:06
So this is the formula for hyperbolic distance.
01:09
Now we need to take each pair of points and we need to find the distance between those two points.
01:17
Now for the let us take the points minus 0 .1 0 .2 and 0 .3 0 .2.
01:26
So it will be x1 y1 x2.
01:30
Now substituting these values in the hyperbolic distance formula.
01:35
So we get d1 dash which is equal to cos h inverse of cause h of y 1 is 0 .2.
01:45
Cause h of x2 is 0 .2 .2.
01:49
Minus x1 is minus 0 .1 so it is plus 0 .1 and into cos h of y2 is 0 .2 minus sign h of y1 is 0 .2 and y sign h of y2 is again 0 .2 so also we know that we can write cos h as e power minus x plus e power x by 2 and sign h as minus e power minus x plus e par x by 2.
02:26
So substituting these values here in this.
02:30
So we get d1 dash to be equal to cos h inverse of e power minus 0 .2 plus e power 0 .2 divided by 2 the whole square into e power minus 0 .4 plus e power 0 .4 divided by 2 minus e power 0 .4 divided by 2 minus e.
02:53
Power 0 .2 minus e power minus 0 .2 divided by 2 the whole square.
03:02
So simplifying this, we get the value of d1 dash to be equal to cos h inverse of 1 .08435.
03:12
So taking simplifying this, we get this value of d1 dash to be equal to 0 .4078.
03:20
Now for the next points, let us take the points as 0 .3, 0 .2 and 0 .1.
03:30
So it will be x1, y 1, x2.
03:33
So now substituting these points in the given formula, so we get d2 dash to be equal to cos h inverse of cause h of 0 .2 into to cause h of minus 0 .3 into cause h of 0 .1 minus sign h of 0 .1 into sign h of 0 .1.
04:12
So simplifying this by the above process.
04:17
So we get the value of d2 dash to be equal to 0 .3125.
04:24
Now let us consider the points minus 0 .1, 0 .2, and 0 .1...
