Semielliptical Arch Bridge An arch in the shape of the upper

Semielliptical Arch Bridge An arch in the shape of the upper half of an ellipse is used to support a bridge that is to span a river 26 meters wide. The center of the arch is 9 meters above the center of the river (see the figure). Write an equation for the ellipse in which the x-axis coincides with the water level and the y-axis passes through the center of the arch. Type the left side of the equation below. = 1 (Simplify your answer.)

Solution

Ellipse is centred at origin

The major axsi is along the x axis .Lenght of major axis = 26

So, length of semi major axis = a= 13

Minor axis is alon y axis and semi minor axis, b, = 9

Gen equation ellipse : x^2/a^2 + y^2/b^2 = 1

x^2/169 + y^2/81 =1