the other focus. AS = . × km, SA ' = km + = - = . × Subtracting c = .
× km Distance of the Sun from the other focus is SS ′ = km. Example . A concrete bridge is designed as a parabolic arch. The road over bridge is m long and the maximum height of the arch is m .
Write the equation of the parabolic arch. From the graph the vertex is at ( , ) and the parabola is open down Equation of the parabola is x = - ay and ( lie on the parabola = - a ( a = x = − Therefore equation is x = - y Fig. . Fig.
. Sun S S' Earth ( ,– ) O (– ,– ) - - Example . The parabolic communication antenna has a focus at m distance from the vertex of the antenna. Find the width of the antenna m from the vertex.
Let the parabola be y = ax . Since focus is m from the vertex a = Equation of the parabola is y = x Let P be a point on the parabola whose x -coordinate is m from the vertex P ( , ) y y = y = = The width of the antenna m from the vertex is m .