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Chapter 10: Q. 40 (page 644)

Find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility.

x2=-4y

Short Answer

Expert verified

The vertex is 0,0focus is 0,-1and the directrix is y=1.

The graph of the equation x2=-4y.

Step by step solution

01

Step 1. Given information .

Consider the given equationx2=-4y.

02

Step 2. Analyze the equation .

The standard form of parabola is x2=-4ay

Compare the equation with standard form.

x2=-4ayx2=-4y-4a=-4a=1

Further simplify.

Since the value of a=1the vertex is 0,0,the focus is 0,-a=0,-1and the directrix isy=a,y=1.

03

Step 3. Plot the graph .

The graph of the equation x2=-4yby using graphic utility just shown below.

Here V is the vertex ,F is focus and liney=1represents the directrix of the parabola .

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Most popular questions from this chapter

Answer Problem using the figure.

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

1. The formula for the distance d from P1=(x1,y1)toP2=(x2,y2)is d = _____.

Semi elliptical Arch Bridge An arch in the shape of the upper half of an ellipse is used to support a bridge that is to span a river 20meters wide. The center of the arch is 6meters above the center of the river. See the figure. Write an equation for the ellipse in which the x-axis coincides with the water level and the y-axis passes through the center of the arch.

In Problem, identify the graph of each equation without completing the squares.

x2+4x+y+3=0

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

Focus at -2,0and directix of the line x=2.
See all solutions

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