00:01
In this question we have to find out the parametric equation for the set of all points p such that distance op is equals to the distance ab.
00:13
Okay so we have been given the curve called as sisoid of diodes.
00:20
Let us draw this curve here.
00:23
So this is the curve that we have been given.
00:26
This is the circle.
00:30
Next we have been given another point here.
00:33
Sorry this is the another line touching the circle.
00:39
Then we are joining these two points.
00:42
This is given to be a and this length here this is ab.
00:51
Here we have p.
00:53
This is o.
00:55
This op length is given to equals to ab length.
00:59
This is the y axis and this is the corresponding x axis.
01:03
This is given to be the line x equals to 2 times of a.
01:07
Let us find out first of all we say that circle has the radius a and center is a comma 0.
01:17
This is a comma 0 is the center of the circle.
01:21
Now this is the point of intersection of the line and the circle.
01:28
This is point c.
01:30
If i write down first of all oc it will be diameter 2 times radius.
01:36
Next we consider cosine of theta.
01:42
So it will be b over h.
01:47
This comes out to be b that is base over hypotenuse.
01:51
Base is oc.
01:53
Hypotenuse comes out to be ob.
01:59
We are talking about the right angle triangle obc.
02:03
We get the following.
02:05
From this we write ob equals to oc over cosine of theta.
02:11
Since oc is given to be 2a this implies ob equals to 2a over cosine theta.
02:20
We call it equation 1.
02:22
Now we consider the right angle triangle oac.
02:31
Correct.
02:34
And let us see what we are going to get.
02:39
This triangle we are going to consider.
02:41
We know that angle subtended by diameter or in a semicircle it is always 90 degree.
02:47
So we consider the triangle oac.
02:53
We get the following.
02:55
Theta is angle of inclination here.
02:57
We get cosine of theta equals to base which is now oa times the hypotenuse which is oc.
03:06
Again we get oa equals to oc cosine theta and oc is 2 times of base.
03:13
So we get this as 2a cosine theta...