 Hello and welcome to the session. In this session we will discuss about the conic section parabola. Basically a parabola is the set of all points in a plane that are equidistant from a fixed line and a fixed point not on the line in the plane. This is a parabola. This fixed line L is called the direct tricks of the parabola and the fixed point this point F is called the focus. And this line through the focus which is perpendicular to the direct tricks is called the axis of the parabola. The point of intersection of the parabola with the axis that is this point is called the vertex of the parabola. Next we will discuss standard equations of parabola. Equation of the parabola with vertex at the origin a0 direct tricks as x equal to minus a is given by y square equal to 4ax. This is the parabola y square equal to 4ax in which we have focus F as a0 direct tricks as x equal to minus a and vertex is the origin o. In this equation we have a is greater than 0 so x can assume any positive value or 0 but no negative value and the curve extends indefinitely far into the first and the fourth quadrants. Axis of the parabola is the positive x axis. Now the other standard equations of parabola are given by y square equal to minus 4ax, x square equal to 4 Ay and x square equal to minus 4 Ay. These are the four standard equations of parabolas. The standard equations of parabolas have focus on one of the coordinate axis that is either on the x axis or y axis. Vertex is at the origin and direct tricks is parallel to the other coordinate axis. Like in this parabola y square equal to 4ax we have focus F with coordinates a0 on the x axis and the direct tricks is parallel to the y axis and the vertex is at the origin. From the standard equations of parabolas we have following observations. The first one says that parabola is symmetric with respect to the axis of the parabola that is if the equation of the parabola has y square term then the axis of symmetry is along x axis. And if the equation of the parabola has x square term in it then the axis of symmetry is along y axis. The next we have when the axis of symmetry is along the x axis then the parabola opens to right if coefficient of x is positive and it opens to left if coefficient of x is negative then we have if the axis of symmetry is along y axis then the parabola opens upwards if coefficient of y is positive it opens downwards if coefficient of y is negative. Next is latest rectum. Latest rectum of a parabola is the line segment perpendicular to the axis of the parabola through the focus whose end points lie on the parabola. This line segment is perpendicular to the axis of the parabola through the focus at end points of this line segment lie on the parabola so this line segment is the latest rectum. For the parabola y square equal to 4ax length of the latest rectum is equal to 4a. Consider the parabola x square equal to 6y this equation of the parabola is of the form x square equal to 4ay. So when we compare these two equations we get 4a is equal to 6 that is we get a is equal to 3 by 2. This is a case of upward parabola so this is the parabola x square equal to 6y where we have focus f is given by 0 comma a that is 0 comma 3 by 2. This is the focus f of the parabola its vertex is the origin then equation of direct tricks is given by y equal to minus a that is minus 3 by 2 that is we have 2y plus 3 equal to 0. This is the direct tricks 2y plus 3 equal to 0. Now since the equation of the parabola has x square term in it so we have its axis would be that is axis of the parabola x square equal to 6y is y axis whose equation is given by x equal to 0. Then length of the latest rectum is given by 4a that is equal to 4 multiplied by 3 by 2 which is equal to 6. This completes the session hope you have understood the concept of the conic section parabola.