Aim:
\[\text{Do the following actives.}\ \hspace{15cm}\]
\[i).\ \text{Draw the graphs of the parabolas}\ (y\ -\ k)^2\ = 4\ a\ (x\ -\ h)\ and\ (x\ -\ h)^2\ = 4\ a\ (y\ -\ k)\ \hspace{10cm}\]\[\text{for the given values of a, h and k}\ \hspace{5cm}\]
\[ii).\ \text{Determine the vertex, focus, axis, directrix, latus rectum of each parabola and}\ \hspace{10cm}\]\[\text{mark them on the graphs.}\ \hspace{2cm}\ \text{[Data set: a = 2, h = 5, k = 2] }\ \hspace{3cm}\]
Procedure
\[\color{green}{Step\ 1:}\ \text{Open Geogebra classic 5 (by double clicking on the icon)}\ \hspace{8cm}\]
\[\color{green}{Step\ 2:}\ \text{Make graph centre}\ \hspace{17cm}\]
\[\color{green}{Step\ 3:}\ \text{To bring Input bar up: right click → Click graphics → Preferences → Layout tab}\ \hspace{3cm}\ \\ \hspace{1cm}\ \text{→ Input Bar → Click show up box}\]
\[\color{green}{Step\ 4:}\ \text{Create the sliders for a, h & K: Tool bar → Slider tool → Click slider →}\hspace{5cm}\\ \hspace{1cm}\ \text{click the mouse cursor in graph →rectangular box open → under name: type ‘a’ → click ok.}\\ \text{ Then set a = 2, h = 5 and k = 2.}\]
\[\color{green}{Step\ 5:}\ \text{To draw the parabola: Input bar → parabola:}\ (y-k)^2\ =\ 4a(x-h)\ \text{→ Enter →}\hspace{5cm}\\ \hspace{1cm}\ \text{right click on parabola → object properties → colour the parabola}\]
\[\color{green}{Step\ 6:}\ \text{To find vertex: Input bar → V:vertex(conic) → V:vertex(parabola) → right click on V →}\\ \text{object properties → Put tick in the check box of Name and value → give colour to V}\]
\[\color{green}{Step\ 7:}\ \text{To find vertex: Input bar → F:focus(conic) → F:vertex(parabola) → right click on F →}\\ \text{object properties → Put tick in the check box of Name and value → give colour to F}\]
\[\color{green}{Step\ 8:}\ \text{To find the distance of focus from vertex: Input bar → d:segment(point; point) →}\hspace{5cm}\\ \hspace{1cm}\ \text{d:segment(V, F)→ right click on d →object properties → Put tick }\\ \text{in the check box of Name and value → give colour to d}\]
\[\color{green}{Step\ 9:}\ \text{To find the Axis: Input bar → Axis:line(point; point) →
Axis:line(V, F)→}\\ \text{right click on Axis →object properties → give colour to Axis}\]
\[\color{green}{Step\ 10:}\ \text{To find the Directrix: Input bar → Directrix:Directrix(conic;) →
}\ \hspace{5cm}\\ \text{Directrix:Directrix(parabola)→ right click on Directrix →object properties → give colour to Directrix}\]
\[\color{green}{Step\ 11}\ \text{To find the Latus Rectum: Tool bar → Select Perpendicular tool → Click F(focus) and Axis)
}\\ \text{→ right click on latus rectum →object properties → give colour to latus rectum}\]
\[\color{green}{Step\ 12:}\ \text{To find the length of Latus Rectum: Tool bar → Select intersection tool → click latus rectum
}\ \hspace{5cm}\\ \text{and parabola→ right click on point B →Put tick in the check box of Name and value}\ \hspace{8cm}\\ \hspace{1cm}\ \text{→ give colour to B → right click on point A →Put tick in the check box}\ \hspace{8cm}\\ \hspace{1cm}\ \text{of Name and value →give colour to A → segment(point : point) }\ \hspace{8cm}\\ \hspace{1cm}\ \text{→ segment(A, B)→ right click on AB →object properties →Put tick}\ \hspace{8cm}\\ \hspace{1cm}\ \text{in the check box of Name and value→ give colour to AB → hide latus rectum}\]
\[\color{green}{Step\ 13:}\ \text{Write all the values from Algebraic view in the output box against first parabola}\\ (y-k)^2 = 4 a (x-h)\ \hspace{8cm}\]
\[\color{green}{Step\ 14:}\ \text{To determine all the values for the second parabola}\ (x-h)^2\ =\ 4a(y-k): \ \hspace{10cm}\\ \hspace{1cm}\ \text{Tool bar→ select Input box under slider tool → Click the mouse cursor in the graph →}\ \hspace{10cm}\\ \hspace{1cm}\ \text{pop up rectangular box opens up → Type “Equation=” under caption → assigned to parabola}\ \hspace{10cm}\\ \hspace{1cm}\ (y-k)^2 = 4*a*(x-h)\ \text{ → Enter → one box pops up → replace the first parabola with}\ \hspace{10cm}\\ \hspace{1cm}\ \text{ second parabola → That’s it → parabola diagram will change →}\ \hspace{10cm}\\ \hspace{1cm}\ \text{as well as its algebraic values → Write all the values from Algebraic view in }\ \hspace{10cm}\\ \text{the output box against first parabola}\ (y-k)^2 = 4 a (x-h)\]
Output:
Output for parabolas
| Equation of the Parabola | ||
| Vertex | (5,2) | (5,2) |
| Focus | (7,2) | (5,4) |
| Distance from vertex to focus | 2 | 2 |
| Axis | y = 2 | x = 5 |
| Directrix | x = 3 | y = 0 |
| Latus rectum | x = 7 | y = 4 |
| Length of latus rectum | 8 | 8 |
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