 Hello and welcome to the session. In this session we will discuss about the conic section hyperbola. Basically a hyperbola is the set of all points in a plane. The difference of whose distance is from two fixed points in the plane is a constant. The hyperbola, the two fixed points that is considered, this point say f1 and this point say f2, these are the foci of the hyperbola. Then the midpoint of the line segment joining the foci that is this point is called the center of the hyperbola. Then the line through the foci that is this line is called the transverse axis and the line through the center and perpendicular to the transverse axis is called the conjugate axis that is this is the conjugate axis. Then the points at which the hyperbola intersects the transverse axis that is these points are called the vertices of the hyperbola. This is the vertex and this also is the vertex of the hyperbola. We denote the distance between two foci that is f1 and f2 by 2c then the distance between the two vertices is given by 2a or we can say that the length of transverse axis is 2a and length of the conjugate axis is given by 2b and this quantity v is given by square root of c square minus a square. Then we have eccentricity which is given by e equal to c upon a or we can say that c is equal to ae since we have c is greater than equal to a so eccentricity e is lever less than 1. In terms of eccentricity we say that the foci are at a distance of ae from the center. Now we discuss some standard equations of hyperbola. This is the hyperbola with foci f1 and f2 coordinates of f1 is given by minus c0 and coordinates of f2 are given by c0. Then these are the two vertices whose coordinates are given by minus a0 and coordinates for this vertex is given by a0. We have equation of hyperbola with origin o00 and transverse axis along x axis is given by x square upon a square minus y square upon b square equal to 1. A hyperbola in which we have a is equal to b is called equilateral hyperbola. Then another standard equation of hyperbola is given by y square upon a square minus x square upon b square equal to 1. From these two standard equations of hyperbola we have some observations like hyperbola is symmetric with respect to both the axis and the foci are always on the transverse axis. Next we discuss latest rectum. Latest rectum of a hyperbola is a line segment perpendicular to the transverse axis through any of the foci and whose endpoints lie on the hyperbola. Like in this case this is the latest rectum of the hyperbola and this line segment is also the latest rectum of the hyperbola. And length of the latest rectum is given by 2b square upon a. Consider the hyperbola x square upon 36 minus y square upon 64 equal to 1. This is of the form x square upon a square minus y square upon b square equal to 1. So when we compare these two we get that a square is equal to 36 and b square is equal to 64. And so from here we have a is equal to 6 and b is equal to 8. C is equal to square root of a square plus b square that is equal to square root of 100 which is equal to 10. Now length of the transverse axis is given by 2a that is equal to 12. Then we have length of conjugate axis is given by 2b and that is equal to 16. Now the coordinates of the vertices are given by say a vertex a with coordinates minus a0 that is minus 6 0 and a vertex b with coordinates a0 that is 6 0. Then we have coordinates of the foci say f1 be given by minus c0 that is minus 10 0 and f2 be given by c0 that is 10 0. A centricity of the hyperbola e is equal to c upon a that is 10 upon 6 and which comes out to be equal to 5 upon 3. Then we have length of the latest rectum is equal to 2b square upon a which is equal to 64 upon 3. This completes the session hope you have understood the conic section hyperbola.