EX-4 – Draw a parabola which fits the image of parabolic shaped bridge and determine the equation, vertex, focus, directrix and latus rectum using geogebra classic 5

\[\text{To draw the graph of given equations of circles}\ \hspace{12cm}\\ x^2\ +\ y^2\ -\ 4x\ +\ 6y\ +\ 8\ =\ 0\ and\ \hspace{5cm}\\ x^2\ +\ y^2\ -\ 4x\ +\ 6y\ +\ 8\ =\ 0\]

\[1.\ \text{To Draw a parabola which fits the given image of parabolic shaped bridge.}\ \hspace{10cm}\]

\[2.\ \text{To write the equation the parabola.}\ \hspace{18cm}\]

\[3.\ \text{To find the vertex, focus, directrix and latus-rectum}\ \hspace{15cm}\\ \text{and mark them on the graph.}\ \hspace{14cm}\]

\[4.\ \text{To find the height and width of parabolic shaped bridge.}\ \hspace{15cm}\]

\[\color{green}{Step\ 1:}\ parabolic\ shaped\ bridge\ image: \text{in Google search engine – type parabolic bridge}\ \hspace{8cm}\\ \hspace{1cm}\ \text{in images → dish antenna png (transparent) → Save as → desktop}\]

\[\color{green}{Step\ 2:}\ \text{Open Geogebra classic 5 (by double clicking on the icon)}\ \hspace{8cm}\]

\[\color{green}{Step\ 3:}\ \text{Make graph centre}\ \hspace{17cm}\]

\[\color{green}{Step\ 4:}\ \text{To bring Input bar up: right click → Click graphics → Preferences → Layout tab}\ \hspace{3cm}\ \\ \hspace{1cm}\ \text{→ Input Bar → Click show up box}\]

\[\color{green}{Step\ 5:}\ \text{To insert parabolic bridge image: Tool bar → Slider tool → click image tool →}\ \hspace{3cm}\ \\ \hspace{1cm}\ \text{insert parabolic bridge image in Graphics view}\]

\[\color{green}{Step\ 6:}\ \text{Two points are provided to control the image, and you can set the}\ \hspace{7cm}\ \\ \hspace{1cm}\ \text{position near to origin such that bridge ends are on the X – axis}\]

\[\color{green}{Step\ 7:}\ \text{Using Algebraic view → hide the two points A & B → Right click on the image →}\ \hspace{5cm}\ \\ \hspace{1cm}\ \text{Object Properties → Back ground image}\]

\[\color{green}{Step\ 8:}\ \text{Create the sliders for a, h & K: Tool bar → Slider tool → Click slider →}\hspace{5cm}\\ \hspace{1cm}\ \text{click the mouse cursor in graph →rectangular box open → under name: type ‘a’ → click ok.}\\ \text{ with minimum – 5 and maximum = 5}\]

\[\color{green}{Step\ 9:}\ \text{To draw the graph of the the parabola by using Input bar → type → parabola:}\ \hspace{5cm}\\ \hspace{1cm}\ (x-h)^2\ = 4*a*(y-k)\]

\[\color{green}{Step\ 10:}\ \text{Adjust the sliders a, h and k to fit the parabola}\ \hspace{11cm}\\ \text{to the given parabolic bridge}\ \hspace{15cm}\]

\[\color{green}{Step\ 11:}\ \text{To plot the vertex of the parabola → type V:vertex(parabola) in the input bar→ right click on V →}\ \hspace{3cm}\\ \text{object properties → Put tick in the check box of Name and value → give colour to V}\]

\[\color{green}{Step\ 12:}\ \text{To plot the focus of the parabola → type F:focus(parabola) in the input bar→ right click on F →}\ \hspace{3cm}\\ \text{object properties → Put tick in the check box of Name and value → give colour to F}\]

\[\color{green}{Step\ 13:}\ \text{To join the points vertex V and focus F: Input bar → VF:segment(point; point) →}\hspace{5cm}\\ \hspace{1cm}\ \text{VF:segment(V, F)→ right click on VF →object properties → Put tick }\\ \text{in the check box of Name and value → give colour to VF}\]

\[\color{green}{Step\ 14:}\ \text{To find the Axis: Input bar → Axis:line(point; point) → Axis:line(V, F)→}\ \hspace{10cm}\\ \text{right click on Axis →object properties → give colour to Axis}\]

\[\color{green}{Step\ 15:}\ \text{To find the Directrix: Input bar → Directrix:Directrix(conic;) → }\ \hspace{10cm}\\ \text{Directrix:Directrix(parabola)→ right click on Directrix →object properties → give colour to Directrix}\]

\[\color{green}{Step\ 16}\ \text{To draw the Latus Rectum: Tool bar → Select Perpendicular tool → Click F(focus) and Axis) }\ \hspace{4cm}\ \\ \text{rename to Latus → right click on latus rectum →object properties → give colour to latus rectum}\]

\[\color{green}{Step\ 17:}\ \text{To find the point of intersention: Tool bar → Select intersection tool → click latus }\ \hspace{5cm}\\ \text{and parabola→ right click on point C →Put tick in the check box of Name and value}\ \hspace{8cm}\\ \hspace{1cm}\ \text{→ give colour to C → right click on point D →Put tick in the check box}\ \hspace{8cm}\\ \hspace{1cm}\ \text{of Name and value →give colour to D → segment(point : point) }\ \hspace{8cm}\\ \hspace{1cm}\ \text{→LR: segment(C, D)→ right click on LR →object properties →Put tick}\ \hspace{8cm}\\ \hspace{1cm}\ \text{in the check box of Name and value→ give colour to LR → hide latus rectum}\]