Chapter 10: Q. 77 (page 645)

Show that an equation of the form $C y^{2} + D x = 0$ where C,D are not equat to 0 is the equation of a parabola with vertex at $(0, 0)$ and axis
of symmetry the x-axis. Find its focus and directrix.

Short Answer

Expert verified

The focus is $(\frac{- D}{4 C}, 0)$ and directrix is $x = \frac{D}{4 C}$ .

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 ${(y - k)}^{2} = 4 a (x - h)$ where h , k are the points of center and x , y are the points of focus .

. Find the equation .

To find the equation of parabola rewrite the given equation in the standard form .

${(y - 0)}^{2} = 4 (\frac{- D}{4 C}) (x - 0)$

Compare this equation with standard form .

$a = \frac{- D}{4 C}$

Since the value of $a = \frac{- D}{4 C}$ ,then the focus is $(0 + a, 0) = (\frac{- D}{4 C}, 0)$ and the directrix is $x = h - a = \frac{D}{4 C}$ .

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Show that an equation of the form $C y^{2} + D x = 0$ where C,D are not equat to 0 is the equation of a parabola with vertex at $(0, 0)$ and axis
of symmetry the x-axis. Find its focus and directrix.

Short Answer

Step by step solution

Step 1. Given information .

Step 2. Standard form of parabola used .

. Find the equation .

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Show that an equation of the form Cy2+Dx=0where C,D are not equat to 0 is the equation of a parabola with vertex at 0,0and axisof symmetry the x-axis. Find its focus and directrix.

Short Answer

Step by step solution

Step 1. Given information .

Step 2. Standard form of parabola used .

. Find the equation .

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Mechanics Maths

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Study anywhere. Anytime. Across all devices.

Show that an equation of the form $C y^{2} + D x = 0$ where C,D are not equat to 0 is the equation of a parabola with vertex at $(0, 0)$ and axis
of symmetry the x-axis. Find its focus and directrix.