 Hello and welcome to the session. Let us discuss the following question. It says an arc is in the form of semi-elips It is 8 meter wide and 2 meter high at the center. Find the height of the arc at a point 1.5 meter from one end So we are given an arc which is in the form of semi-elips so let The upper part of the ellipse be be the given arc Now the general equation of the ellipse given by 1 a square plus y square upon b square is equal to 1 where And we are given that this arc is 8 meter wide So half of this that the semi-major axis is is 4 meter 8 by 2 that is 4 meter and V is the semi-minor axis that is this And we are given that it is 2 meter high from the center. So it is 2 meter So the equation of the ellipse so it becomes n plus y square upon 4 is equal to 1 Now we have to find the height of the arc at a point 1 point So if D is this point which is 1.5 meter From the end point A and we have to find this so let this be distanced denoted by dd dash Where d dash is any point on the arc Now we are given that Distance of this point from one of the end is 1.5 meter That is ad is 1.5 meter O which is the semi-major axis is 4 meter then od is equal to A o minus Od od is equal to A o minus Ad minus 1.5 meter Which is equal to 2.5 meter So here the coordinate of D Point D is 2.5 0 0.5 now we put x is equal to 2.5 in this and we'll get the value of y So from we have 2.5 square upon 16 plus y square upon 4 is equal to 1 simplifying this we get 6.25 plus 4 y square is equal to 16 and this implies y square is equal to 16 minus 6.25 upon 4 and This implies y is equal to under the root of 9.75 upon 4 which is equal to 1.56 Approximately so here the coordinates of the point D dash are 2.5 1.56 That is why coordinate is 1.56 which is the height 1.56 Meter approximately this completes the question by for now take care. Have a good day