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Chapter 10: Q. 35 (page 644)

Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand .

Focus at -3,-2; directrix the line x = 1

Short Answer

Expert verified

The equation of the parabola is y2=8xand the points that determine latus rectum are 2,12,-2,12.

The graph of the equation shown below .

Step by step solution

01

Step 1.  Given information .

Consider the given focus and the line of directrix .

02

Step 2. Equation of parabola used .

A parabola whose focus is at -3,-2and whose directrix line is x=1has its vertex -1,-2. Since the focus is on the negative y axis then the equation of parabola is of the formy2=-4ax.

03

Step 3.  Find the equation of parabola .

To find the equation of parabola substitute the values in the equation .

Here a=-2

y2=-4axy2=-4路-2xy2=8x

Further simplify .

role="math" localid="1647157860145" Substitute y=-2in the equation .

y2=-4ax-22=-4路-2xx=12

Further simplify.

y2=-4axy2=-4路-2路12y2=卤2

Therefore the two points that define latus rectum are2,12,-2,12.

04

Step 4.  Plot the graph .

The graph of the equation y2=8xis shown below .

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Most popular questions from this chapter

In Problems 43鈥�52, identify the graph of each equation without applying a rotation of axes.

3x2-2xy+y2+4x+2y-1=0

Answer Problem using the figure.

If a = 4, then the equation of the directrix is______ .

The graph of a parabola is given. Match each graph to its equation.

A hyperbola for which a=bis called an equilateral hyperbola. Find the eccentricity eof an equilateral hyperbola.

[Note: The eccentricity of a hyperbola is defined in Problem 81.]

Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.

Vertex is at4,-2and focus is at6,-2.
See all solutions

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