 Hi and welcome to the session my name is Priyanka and I am going to help you with the following question. It says find the equation of the normal at the points a m square a m cube for the curve a y square equal to x cube. Let us rewrite the equation of the curve once again. Now I am differentiating with respect to x the above given equation we get 2 a y d y by d x equal to 3 x square. This implies we have the value of d y by d x equal to 3 x square upon 2 a y right. Now at point a m square a m cube we have the value of d y by d x equal to 3 a m square the whole square upon 2 a a m cube which gives us 3 a square m raised to the power 4 upon 2 a square m cube we are left with 3 m upon 2. Now we can find slope of normal we know that the formula for finding slope of the normal is minus 1 upon d y by d x right that is minus 1 upon 3 m by 2 which gives us the answer as minus 2 upon 3 m this is the slope for the normal. Now we can easily find out equation of the normal equation of normal is y minus y 1 now here in the question we are given y 1 as a m cube equal to slope of the normal x minus x 1 solving it very carefully we have 3 m y minus we are multiplying 3 m by this 3 a m raised to the power 4 equal to minus 2 x plus 2 a m square. Now since it cannot be further simplified let us take all the terms to the left hand side we have 2 x plus 3 m y is to minus now from these 2 when it is being taken here we can take minus a m square common we will be left with 2 plus 3 n raised to the power square equal to 0 right this is the answer for the question which is given to us let me rewrite it for you all it is 2 x plus 3 m y minus a m square bracket 2 plus 3 m square equal to 0 this is the slope sorry the equation of the normal at the points a m square a m cube for the curve a y square equal to x cube this completes the session hope you understood the simplification well take care while proceeding the solution and have a very nice day ahead.