Sketch the three basic conic sections in standard position with vertices and foci on the x-axis.

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Step 1 The basic three conic sections are parabola. ellipse and hyperbola. The standard equation of the parabola having its vertex and focus on the x-axis is y2=4ax. The focus of the parabola is (a, 0) and the vertex is (0, 0). Sketch the graph of the parabola y2=4ax as shown below.   From the above figure, it is observed that the standard parabola is symmetric about x-axis and opening right side. Step 2 The standard equation of the ellipse having its vertices and foci on the x-axis is x2a2+y2b2=1. a2=b2+c2 The vertices of the ellipse are (± a, 0) and the foci are (± c, 0). Draw the ellipse x2a2+y2b2=1 as shown below.  From the above figure, it is observed that the ellipse has the x-axis as the major axis and the y-axis as the minor axis. And it is called the horizontal ellipse. Step 3 The standard equation of the hyperbola having its vertices and foci on the x-axis is x2a2−y2b2=z. b2=c2−a2. The vertices of the hyperbola are (± a, 0) and the foci are (± c, 0) Draw the hyperbola x2a2−y2b2=1 as shown below.  From the above figure, it is observed that the hyperbola has the x-axis as major axis and the y-axis as a minor axis.

Sketch the three basic conic sections in standard position with vertices and foci on the x-axis.

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