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Chapter 10: Q 23. (page 643)

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.

Short Answer

Expert verified

The equation of a parabola is y2=-8x. The points are -2,4and -2,-4. The graph of an equation is :

Step by step solution

01

Step 1. Given Information.

The given focus of an equation be-2,0and an equation of its directix of a line bex=2.

02

Step 2. Equation of a parabola.

The vertex of an equation be at 0,0. The vertex is midway between the focus and the directix. Since, the focus is on the x-axis at -2,0, the equation of the parabola is f the form

role="math" localid="1646657517636" y2=4axwith a=-2.

i.e.y2=-8x.

03

Step 3. Latus rectum.

The points that determine the latus rectum by letting x=-2.

y2=-8xy2=-8-2y2=16y=卤4.

The points are-2,4and-2,-4.

04

Step 4. Graphing utility.

The graph of an equation y2=-8xwill be

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Most popular questions from this chapter

In Problems 31鈥� 42, rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation. Refer to Problems 21鈥�30 for Problems 31鈥� 40.

x2-4xy+y2-3=0

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

y2=8x

True or False

The equation ax2+6y2-12y=0defines an ellipse if width="36">a>0

Except for degenerate cases, the equationAx2+Bxy+Cy2+Dx+Ey+F=0defines an ellipse if ________ .

If 胃is acute, the Half-angle Formula for the cosine function iscos胃2=_______.
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