 Hello and welcome to the session. In this session we will discuss about loci. loci is the plural of locus. Let us first discuss what is locus. This is basically a collection of points or given condition. So we can say that locus of a point, a point moves a given condition, conditions. The locus of a point can be straight line and from this definition of the locus, we conclude two things. Every point lying on the locus, a straight line or a curve, the given conditions and also the given conditions will lie which could be a straight line or a curve. So locus is one condition in which we have which lies in a plane. We have another point which moves around from it, moves around x3 and so on the different positions of the point x then it moves around this fixed point o. So by the condition which is given to us we have that this point x moves around this fixed point o at a constant distance would be equal to o x1 would be equal to o x2 would be equal to o x3 and so constant distance would be equal to say a on such point that is x, x1, x2, x3 and so on will lie on the circle and the radius of the circle would be a from this we can conclude and let us discuss the condition we have in pq distance above and below the straight line pq. Now as we know length of the perpendicular from that point on that line. So every points which are a constant distance from the straight line pq in the plane will be on the straight lines on the both sides of the straight line pq and those two lines would be parallel to pq of these lines xy and ab these both lines parallel to the given straight line pq as you can see xy is above the line pq and ab is below the line pq also these two lines constant distance straight line pq case we can say that xy and ab these two lines are the required local when they are given a straight line and a point which is at a constant distance from the given straight line is considered this condition is this we have a straight line pq and a moving point so we can say at a constant distance from the given straight line pq another condition we are given the point moves in the plane or ways remain and q and we have this point which moves such that its distances from p and q always remain equal x moves to x1 the distance of x1 from p and q would also be equal that is dx would be equal to qx and would be equal to qx1 so we can conclude that the milk is softening joining the two fixed points that is in this case it would be the perpendicular bisector of pq we want to the other condition we are given the angle moves at equal distances pqr and the arms of the angle pq and qr in definite lengths so these angles that is pq and qr are of indefinite lengths we have a point under pqr and this point x moves at equal distances from pq and qr so this distance would be equal the same way if the position of this point x is this distance would be equal so we can say that the locus of the given angle we will discuss how to find the locus of a point we can do this by two methods first method is reasoning locus of a point from the locus then also we prove now we have another method to find the locus of a point and that method is by plotting the points when the first method reasoning or guess work this method we plot and join them to obtain the locus when we get the if that locus is correct or not by checking that every point on the locus satisfies the given conditions and if all the points satisfy the given condition then they should lie on the locus next we have the points of intersection of loci the point of the conditions lies on the point of intersection those loci of which locus of that point given conditions given a point which satisfy many different conditions then this point would lie on the point of intersection of those loci which are the locus of this point according to the given conditions