 Hi and welcome to the session. Let us discuss the following question. The question says find the direction in which a straight line must be drawn through the point minus one two so that its point of intersection with the line x plus y is equal to four may be at a distance of three units from this point. Let this be a line which is drawn through the point p having coordinates minus one two. Let a be be a line whose equation is x plus y is equal to four. This line is intersecting a be at point q and the distance of point p from q is three units. We have to find direction of line pq that means we have to find slope of this line. Let us now begin with the solution. Let m be the slope of line pq so equation of pq is y minus two is equal to m into x plus one. Now this implies y is equal to mx plus m plus two. Let us name this equation as equation number one. Now since both these lines intersect at point q so we can find the coordinates of point q by solving the equation of lines pq and ab simultaneously. Now equation of line ab is x plus y is equal to four. Now from one we know that y is equal to mx plus m plus two so substitute the value of y in this equation. Substituting the values we get mx plus m plus two plus x is equal to four. This implies one plus m into x is equal to four minus m minus two. This implies x is equal to two minus m upon one plus m. Now we will find the value of y so put the value of x in one. By substituting the values we get y is equal to m into two minus m upon one plus m plus m plus two. This is equal to two m minus m square plus m plus m square plus two plus two m upon one plus m and this is equal to five m plus two upon one plus m. So coordinates of point q are minus m upon one plus m and five m plus two upon one plus m. In the question we are given that distance between pq is equal to three units. Now by using distance formula pq is equal to square root of two minus m upon one plus m plus one whole square plus two plus five m upon one plus m minus two whole square and this is equal to three by one plus m whole square plus three m upon one plus m whole square and this is equal to nine plus nine m square upon one plus m whole square. Now substitute the value of pq, pq is equal to three units so now we have three is equal to square root of nine plus nine m square upon one plus m whole square square in both sides we get nine into one plus m whole square is equal to nine plus nine m square this implies nine plus nine m square plus eighteen m is equal to nine plus nine m square and this implies eighteen m is equal to zero and this implies m is equal to zero. Now m is equal to zero implies slope of line pq is zero and this implies that the line has parallel to x axis so slope of line pq is zero this means line is parallel to x axis this is a required answer so this completes the session bye and take care