Chapter 10: Q. 76 (page 645)

Show that an equation of the form $A x^{2} + E y = 0$ is the equation of a parabola with vertex at $(0, 0)$ and axis of symmetry the y-axis. Find its focus and directrix.

Short Answer

Expert verified

The focus is $(0, \frac{- E}{4 A})$ , and equation of directrix is $y = \frac{E}{4 A}$ .

Step by step solution

Step 1. Given information .

Consider the given equation and vertex .

Step 2. Standard form of parabola used .

The standard form of parabola is ${(x - h)}^{2} = 4 a (y - k)$ .

Step 3. Find focus and directrix.

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

${(x - 0)}^{2} = 4 (\frac{- E}{4 A}) (y - 0)$

Compare this equation with standard form .

$a = \frac{- E}{4 A}$

Therefore the focus is $(0, 0 + a) = (0, \frac{- E}{4 A})$ and the line of directrix is $y = h - a = 0 - \frac{- E}{4 A} = \frac{E}{4 A}$

Step 4. Plot the graph .

The graph of the equation shown below .

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Show that an equation of the form $A x^{2} + E y = 0$ is the equation of a parabola with vertex at $(0, 0)$ and axis of symmetry the y-axis. Find its focus and directrix.

Short Answer

Step by step solution

Step 1. Given information .

Step 2. Standard form of parabola used .

Step 3. Find focus and directrix.

Step 4. Plot the graph .

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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

Step by step solution

Step 1. Given information .

Step 2. Standard form of parabola used .

Step 3. Find focus and directrix.

Step 4. Plot the graph .

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

Show that an equation of the form $A x^{2} + E y = 0$ is the equation of a parabola with vertex at $(0, 0)$ and axis of symmetry the y-axis. Find its focus and directrix.