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Chapter 10: Q. 76 (page 645)

Show that an equation of the form Ax2+Ey=0is the equation of a parabola with vertex at 0,0and axis of symmetry the y-axis. Find its focus and directrix.

Short Answer

Expert verified

The focus is 0,-E4A, and equation of directrix isy=E4A.

Step by step solution

01

Step 1. Given information .

Consider the given equation and vertex .

02

Step 2. Standard form of parabola used .

The standard form of parabola isx-h2=4ay-k.

03

Step 3. Find focus and directrix.

To find the focus and directrix rewrite the given equation in the standard form.

x-02=4-E4Ay-0

Compare this equation with standard form .

a=-E4A

Therefore the focus is0,0+a=0,-E4Aand the line of directrix isy=h-a=0--E4A=E4A

04

Step 4. Plot the graph .

The graph of the equation shown below .

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