 Hello and welcome to the session let us discuss the following question it says an arc is in the form of parabola with its x is vertical the arc is 10 meter high and 5 meter wide at the base how wide is it 2 meter from the vertex of the parabola. So here we are given a parabola with x is vertical and it is 10 meter high and 5 meter wide that is pq has length 5 meter. So let us now move on to the solution with this information and here equation of parabola is given by x square is equal to minus 4a y here height of the arc is 10 meter which is o m and that is the y. Now pq is the width of the base and pq is given to be 5 meter and the coordinate of the point q are x y where y is 10 is given by mq which is half of pq 2 which is 2.5 meter. So here the coordinate of the point q is 2.5 10. Now we have to find the width when meter from the vertex we have to find this width and here y is 2 meter. So to find the width we first find the value of a from a 5 square is equal to minus 4a y where y is 10 meter and this implies a is equal to minus 6.25 upon 40. Now we have to find the coordinate of when y is 2.4 a y where a is minus 6.25 upon 40 and y is 2. So this implies 10.25 and this implies 10.9 approximately. This point is q dash then the coordinates of q dash are 1.119 and 2 because here y coordinate is 2 and x coordinate is 1.119. Now we have to find the width when the parabola is 2 meter from the vertex that is we have to find p dash q dash. So p dash q dash is double 2x so it is 2 into 1.119 which is equal to 2.23 meter approximately. This completes the question and that's all for the session goodbye and take care.