 Hello and welcome to the session. My name is Asha and I shall be helping you with the following question that says In each of the exercises one to nine find the coordinates of the pokai The vertices the length of major axis the minor axis the eccentricity and the length of latest rectum of The ellipse the first one is x square upon 36 plus y square upon 16 is equal to 1 So first let us learn Something about ellipse Now ellipse is the set of all the points in the plane the sum of whose distances from two fixed point in the plane is constant Suppose this diagram represents ellipse Here ellipse shown has major axis along the x axis Some parameters of ellipse are also shown in this figure f1 and f2 are the pokai Line a b is the major axis and cd is the minor axis points a and b are the vertices here a Is the length of semi major axis? therefore to a that is this a plus a is equal to the major axis similarly b is equal to the length of semi minor axis therefore 2b is equal to the minor axis and c is Equal to the distance of focus from the center is equal to root over a square minus b square Now the standard equation of a ellipse Whose major axis is along the x axis is upon a square plus y square upon b square is equal to 1 and this is if the major axis is Alone the x axis well a is the length of semi major arc and b is the length of semi minor arc and C is the distance of focus from the center which is given by root over a square minus b square and the vertices plus minus a comma 0 and the two focuses are This and this f1 and f2 which are given by plus minus c comma 0 Also, we have to find the eccentricity Which is given by c upon a and it is denoted by e and the length of the latest rectum is equal to two times of b square upon a So this is some general information About the ellipse with the help of these few ideas. We are going to solve the above problem. So this is our key idea. Let's now start with the solution and We are given x square upon 36 plus y square upon 16 is equal to 1 which is the equation of an ellipse now Here this can further be written as x square upon 6 square Plus y square upon 4 square is equal to 1 and on comparing this with the standard form of the equation of an ellipse we find here that a is equal to 6 and d is equal to 4 Now here the denominator of this first x square upon 6 square is More than the denominator of this y square upon 4 square Thus the major axis is along the x axis Since the denominator of x square is greater Therefore, we have major axis is along the x axis Now let us proceed further Now comparing the given equation. We find that a is equal to 6 and b is equal to 4 now. Let us find c This is equal to root over a square minus b square So on substituting the values we have 6 square minus 4 square and this is equal to root over 20 Therefore the first thing we have to find as the coordinates of the 4k So that is given by plus minus root over 20 comma 0 Now we have to find the vertices And as we have done in the key idea vertices are plus minus a comma 0 and here a is equal to 6 So we have plus minus 6 comma 0 Next we have to find the length of Major axis is equal to two times of a so we have two into six and this gives 12 and Similarly, we have to find the length of minor axis which is given by two into b So we have two into four is equal to eight now we have to find the eccentricity and It is given by on a that is root over 20 upon 6 and lastly we have to find the length of latest victim The length of latest victim Is equal to two times of b square upon a so we have two Into four square upon six and this gives Two into sixteen upon six which is for the equal to sixteen upon three so this is the length of the latest victim and Hence our answer is The focus of the given equation Denoting it by f is given by plus minus root over 20 comma 0 its vertices are plus minus 6 comma 0 the length of its major axis is Equal to 12 and the length of minor axis is 8 and eccentricity as we have denoted it and the key ideas e is Equal to root over 20 upon 6 and the latest victim Equal to 16 upon 3 so this completes the session. Hope you have understood it. Take care and have a good day