 Hello and welcome to the session. In this session we will discuss a question which says that Find the vertex, focus, directrix and the axis of the parabola x square is equal to 4a into y minus a the whole also sketch the curve. Now before starting the solution of this question you should know some results. And that is for the parabola x square is equal to 4a y the coordinates of the vertex 0,0 then the coordinates of focus are 0 in when equation of directrix is y is equal to minus a and equation of the axis is x is equal to 0. Now these results will work out as a key idea for solving this question. And now we will start with the solution. Now the equation of the parabola is given to us. Now point is equal to 4a into y minus a the whole minus 0 whole square is equal to 4a into y minus a the whole. We will express this equation in the standard form is not in the standard form. So to express this equation in the standard form of the equation of parabola minus this beta by putting capital x is equal to x plus minus alpha and capital y is equal to y plus minus beta. That is if beta are positive here then we will shift the origin to minus alpha minus beta by putting capital x is equal to x plus alpha and capital y is equal to y plus beta. If beta and alpha are negative here then we will shift that plus beta by putting capital y is equal to x and capital y is equal to y minus beta. Now for this case we will shift the origin to 0 by putting x minus 0 capital y is equal to y minus beta. So we will put these values in equation number 1 and we get x square is equal to capital y. To find out the vertex focus directly across the equation of the form x square is equal to 4a y. So using this result which is given in the key idea we will find the vertex of this parabola is equal to 0. It is equal to y minus equal to 0 which implies 0 implies equal to 0 which implies y is equal to n. Therefore which is given in the key idea. Now we will look at this capital x is equal to 0 and capital y is equal to n. Now capital x is equal to x minus equal to y minus n. 0 is equal to 0 which implies x is equal to 0. A implies y minus a is equal to a which implies y is equal to 2a. Therefore which is given in the key idea we will find the directly equation of the electric is equal to minus a. Now y is equal to minus a implies y minus a. So this will be equal to minus a and this implies y is equal to therefore which is given in the key idea equal to 4a y. Now the equation is equal to 0. Now capital x is equal to 0 implies now capital x is equal to x minus 0. So this will be equal to 0 which implies x is equal to 0 a. After given parabola which is an upper parabola let's focus 0 to n y times 0 a is the equation of the dielectric is y is equal to 0. This is the equation of the given question and that's all for this session. Hope you all have enjoyed this session.