 Hi and welcome to the session. Let us discuss the following question. The question says, in each of the following exercises 1 to 6, find the coordinates of the focus, axis of the parabola, the equation of the length of the latest rectum. Given equation of parabola is y square equals to minus 8x. Before solving this question, we should note 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 the fixed point is called the focus. A line through the focus and perpendicular to the directrix is called the axis of the parabola. The point of intersection of parabola with an axis is called the vertex of the parabola. The latest rectum of a parabola is a line segment which is perpendicular to the axis of the parabola which passes through the focus and whose end points lie on the parabola. Now you should know about standard equations of parabola. The equation of parabola with focus at a0 and directrix x equals to minus a is y square equals to 4ax. Equation of parabola with focus at minus a0 and directrix x equals to plus a is y square equals to minus 4ax. Equation of parabola with focus at 0a and directrix y equals to minus a is x square equals to 4a y. Equation of parabola with focus at 0 minus a and directrix y equals to a is x square equals to minus 4a y. Always remember these standard equations of parabola. From these standard equations we can conclude that if the equation has a y square term then the axis of symmetry is along the x axis and if the equation has an x square term then the axis of symmetry is along the y axis. 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. Now when the axis of symmetry is along the 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 keeping all these things in mind let's now begin with the solution. Given equation of parabola is y square equals to minus 8x. We have learnt that if the equation has a y square term then the axis of symmetry is along the x axis. Now here equation of parabola involves y square so axis of symmetry is along the x axis. We know that if coefficient of x is negative then the parabola opens to the left. Now here coefficient of x is negative and parabola to the left. Now the given equation that is y square equals to minus 8x can be written as y square equals to minus 4 into 2 into x. Now clearly this equation is of the form y square equals to minus 4ax so on comparing y square equals to minus 4 into 2 into x with y square equals to minus 4ax we find that a is equal to We have learnt that if equation of the parabola is of the form y square equals to minus 4ax then its focus is at the point minus a0 and direct x is x equals to plus a. Now here equation of the parabola is of the form y square equals to minus 4ax so focus of this parabola minus a0 and this is equal to minus 2 0 as a is equal to 2. Now equation of direct x is x equals to a. Now here a is equal to so equation of direct x of the given parabola equals to. Now we will find length of latest vector length of latest vector is equal to 4a. Now here a is equal to 2 so length of latest vector of the given parabola is 4 into 2 and this is equal to 8. So coordinates of the focus are minus 2 0 so symmetry is y axis direct x sorry axis of symmetry is x axis equals to 2. Length of latest vector are required answer so this completes the session bye and take care.