 Hi and welcome to the session. Let us discuss the point in question. The question says in each of the coding exercises 1 to 6 find the coordinates of the focus, axis of the parabola, the equation of the directorates and the length of the latest vector. Given equation of parabola is pi square is equal to 12 h. Before solving this question we should know that what is meant by a parabola. A parabola is the set of all points in a plane that are equidistant from a fixed line and a fixed point in the plane. The fixed line is called the directrix of the parabola and fixed point let's say f is called focus of the parabola. A line through the focus and perpendicular to the directrix is called axis of the parabola. The point of intersection of parabola with the axis is called the vertex of the parabola. Our latest rectum of a parabola is the line segment perpendicular to the axis of the parabola through the focus and whose end points lie on the parabola. This is the latest rectum of the parabola. Now we are going to learn about standard equations of parabola. Now look at this figure if the parabola has vertex at the origin focus at the point a0 and directrix x equals to minus a. Then equation of parabola is of the point y square equals to 4ax. Now look at this figure if the vertex of the parabola is at the origin focus at the point minus a0 and directrix x equals to plus a. Then equation of parabola is of the point y square equals to minus 4ax. this figure. If the vertex of the parabola is at the origin focus at the point 0-A and the matrix y equals to minus-A then equation of parabola is of the form x square equals to4a y. Now look at this figure if the vertex of the parabola is at the origin focus at the point zero minus-A and the matrix y equals to A then equation of parameter is of the form x square equals to minus 4a y. So always remember these four equations of parabola. We can conclude from the standard equations of parabola that if equation of parabola has y squared term then axis of symmetry is along y, sorry x axis and if the equation of parabola has x squared term then axis of symmetry is along y axis. Now when the axis of symmetry is along the x axis then the parabola opens to the right if the coefficient of x is positive and parabola opens to the left if the coefficient of x is negative. 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 is the coefficient of y is negative. Giving all this in mind, let's now begin with the solution. Given equation of parabola is y square equals to 12 x. We have learned that if equation of parabola has y square term, then the axis of symmetry is a lot x-axis. Now here the given equation involves y square. So the axis of symmetry is the x-axis. We have also learned that if coefficient of x is positive, then parabola opens to the right. Now here, coefficient of x is positive, parabola opens to the right. Now the given equation y square equals to 12 x can be written as y square is equal to 4 into 3 into x. Now this equation is clearly of the form y square equals to 4 a x. So comparing y square equals to 4 into 3 into x with y square equals to 4 a x. We get a as 3. We have learned that if equation of parabola is y square equals to 4 a x, then its coordinates of the focus are of the form a 0. And equation of directrix is of the form x equals to minus a. Now here the equation of parabola is of the form y square equals to 4 a x. So focus of this parabola is a 0 and here a is equal to 3. So focus of this parabola is 3 0. Equation of directrix x equals to minus 3. Now we will find length of latest rectum. Length of latest rectum is equal to 4 times a. Now here a is equal to 3. So length of latest rectum of this parabola is 12. So coordinates of the focus are 3 0, parabola is x axis, directrix x equals to minus 3. And length of the latest rectum 12. This is our required answer. So this comes to the end of the explanation. Bye and take care.