 Hi and welcome to the session. Let us discuss the following question. The question says, in each of the coordinate exercises 1 to 6, find the coordinates of the focus, axis of the parabola, the equation of the dielectric and the length of the latest rectum. The equation of parabola is x square equals to 6 y. Before solving this question, we should know that what is meant by a parabola. A parabola is the set of all points in a play that are equidistant from a fixed line and a fixed point. And this fixed point is not on the line in the play. The fixed line is called the directrix of the parabola and the fixed point is called the focus of the parabola. A line through the focus and perpendicular to the directrix is called the axis of the parabola. The point of intersection of parabola with the axis is called vertex of the parabola. Latest rectum of a parabola is a line segment perpendicular to the axis of parabola through the focus and whose end points lie on the parabola. Length of this latest rectum is 4a. Now you should know about standard equations of parabola. If the focus of the parabola is at point a0 and directrix is x equals to minus a, then equation of parabola is y square equals to 4ax. If the focus of the parabola is at point minus a0 and directrix is x equals to plus a, then equation of parabola is y square equals to minus 4ax. If focus of the parabola is at point 0a and directrix is y equals to minus a, then equation of the parabola is x square equals to 4 a5. And if focus is at point 0 minus a and directrix is y equals to a, then equation of parabola is x square equals to minus 4 a5. And in all these cases, vertex of the parabola is at the origin. So always remember these four standard equations of parabola. We can conclude from the standard equations of parabola that if the equation has y squared term, then the axis of symmetry is along the x axis. And if the equation has an x squared term, then the axis of symmetry is along y axis. When the axis of symmetry is along x axis, then the parabola opens to the right if the coefficient of x is positive. And if coefficient of x is negative, then parabola opens to the left. Now when the axis of symmetry is along y axis, then the parabola opens upwards if the coefficient of y is positive. And parabola opens downwards if the coefficient of y is negative. So remember all this as this will be helping us to solve the questions. Let's now begin with the solution. Given equation of parabola, square equals to 6y. We have learnt that if the equation has x squared term, then the axis of symmetry is along y axis. Now here the equation involves x squared term. So the axis of symmetry is y axis. So as the equation involves x squared term, therefore the axis of symmetry is y axis. Now here the coefficient of y is positive. We know that if the coefficient of y is positive, then parabola opens upwards. Now here the coefficient of y is positive. So the parabola opens. Now given equation of parabola is x squared equals to 6y. 6y can be written as 4 into 3 by 2 into y. Now clearly this equation is of the form x squared equals to 4y. So on comparing x squared equals to 4 into 3 by 2 into y with x squared equals to 4 a y. We find that a is equal to 3 by 2. We know that if the equation of the parabola is of the form x squared equals to 4 a y, then its focus is at the point 0 a and direct axis y equals to minus a. Now here the equation is also of the form x squared equals to 4 a y. So focus of the parabola 0 a is equal to 3 by 2. So focus of the parabola x squared equals to 6y is 0 3 by 2. Equation of characteristics y equals to minus 3 by 2. Find length of latest vector. We know that length of latest vector is 4 a. Now here a is equal to 3 by 2. So length of latest vector of the parabola x squared equals to 6y is 4 into 3 by 2 and this is equal to so coordinates of the focus are 0 3 by 2 of symmetry is y axis equals to sorry y equals to minus 3 by 2 and length of latest vector this is our required answer. So this completes the session. Bye and take care.