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

York

York

Answered question

2021-08-10

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

Answer & Explanation

comentezq

comentezq

Skilled2021-08-11Added 106 answers

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.
image

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.
image 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
x2a2y2b2=z. b2=c2a2.
The vertices of the hyperbola are (± a, 0) and the foci are (± c, 0)
Draw the hyperbola x2a2y2b2=1 as shown below.
image

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.

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