 Hello everyone, how are you all today? My name is Priyanka and let this question say, 5 points on the curve x square upon 9 plus y square upon 16 is equal to 1 at which the tangents are parallel to x axis, parallel to y axis. Let's start with the solution. Let us first solve it for the first part. We are given the curves equation as x square upon 9 plus y square upon 16 equal to 1. Now, let us first differentiate the above equation with respect to x. And on doing so, we get 2x upon 9 plus 2 upon 16 y into dy by dx equal to 0. That is the derivative of a constant is equal to 0 or we have dividing the whole equation by 2. We have x upon 9 plus y upon 16 dy by dx equal to 0 or we have dy by dx equal to minus x upon 9 into 16. That is, dy by dx is equal to minus 16x upon 9. Now since tangent is parallel to x axis, that means dy by dx is equal to 0. Therefore, we have dy by dx as minus 16 upon 9x equal to 0 which gives us the value of x as 0. And now when the value of x is 0, the value of y is 0 plus y square upon 16 is equal to 1 or y square upon 16 is equal to 1 or y square is equal to 16 or y is equal to plus minus 4. So, hence the points are 0 plus minus 4. Now for the second part, we are given that the tangent is parallel to y axis. That means dy by dx is equal to infinity. That is minus 16x upon 9 y is equal to infinity. Or we have 9y equal to, this infinity is equal to 1 by 0, so we have 9y is equal to 0 or y is equal to 0. Now when y is equal to 0, then the value of x is x square upon 9 is equal to 1, x square is equal to 9, x is plus minus 3. So, the points plus minus 3 comma 0. And let us write the answer once again 0 comma plus minus 4 for the first part and plus minus 3 comma 0 for the second part. Hey, this completes the session. Hope you understood it and have a nice day.