 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 1 to 9, find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of latest rectum of the ellipse. So, let's start with the solution and the 9 to 1 is 4 x square plus 9 y square is equal to 36. So, the given equation of the ellipse, which is 4 x square plus 9 y square is equal to 36 can be rewritten as dividing both sides by 36, x square upon 9 plus y square upon 4 is equal to 1 or x square upon 3 square plus y square upon 2 square is equal to 1. Now, as we can see the denominator of x square upon 9 is greater than the denominator of y square upon 4, thus the major axis is along the x axis and the standard equation of an ellipse whose major axis is along the x axis is given by x square upon a square plus y square upon b square is equal to 1. And please refer to number 1 of this size to know the standard equation of the ellipse and to find the foci, the length of major and minor axis, the vertices, the eccentricity and the length of latest rectum of the ellipse. Now, I am comparing the standard equation of ellipse with the given equation of ellipse we find here that a is equal to 3 and b is equal to 2. Now, let us find c to the equal to root over a square minus b square that is 9 minus 4 which is equal to root over 5 and now let us find the foci which is given by plus minus c comma 0. So, we have plus minus root over 5 comma 0. Now, let us find the vertices of the given ellipse. So, this is equal to plus minus a comma 0 and the a is 3. So, the vertices are plus minus 3 comma 0 and the length of 2 into a. So, we have 2 into 3 which is equal to 6 and length of minor axis is given by 2 b. So, we have 2 into 2 is equal to 4. Now, let us find the eccentricity is equal to c upon a and here c is root over 5 and a is 3. So, this is the eccentricity root 3 upon sorry root 5 upon 3 and lastly let us find the length of latest rectum which is given by 2 into b square upon a that is 2 into 2 square upon a is 3. So, we have 8 upon 3. Hence, our answer is the focus of the equation ellipse are root 5 comma 0 and minus root 5 comma 0. So, the foci are plus minus root 5 comma 0 the vertices are plus minus 3 comma 0 the major axis its length is 6 and the length of the minor axis is equal to 4. It is eccentricity which is denoted by small a is root over 5 upon 3 and the length of the latest rectum is 8 upon 3. This is the latest rectum. So, this completes this equation. Hope you have understood it well. Take care and have a good day.