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Chapter 10: Q 29. (page 643)

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

Vertex at 2,-3and focus at2,-5.

Short Answer

Expert verified

The equation of a parabola is

x-22=-8y+3.

The points are 6,-5;-2,-5.

The graph of a parabola is

Step by step solution

01

Step 1. Given Information.

The given vertex is at the point2,-3and focus is at the point2,-5.

02

Step 2. Equation of a parabola.

The vertex 2,-3and focus 2,-5 both lie on the vertical linex=2(the axis of symmetry). The distance a from the vertex to the focus is a=2.

The parabola opens down to the right.

The form of an equation is

x-h2=-4ay-k

where h,k=2,-3and a=2.

Therefore, the equation is

x-22=-4ay--3x-22=-4ay+3.

03

Step 3. Latus Rectum.

The points that determines the latus rectum by letting y=-5. Then,

localid="1646907557605" x-22=-8y+3x-22=-8-5+3x-22=-8-2x-22=16x-2=卤4x=4+2;x=-4+2x=6,-2

The points are6,-5;-2,-5.

04

Step 4. Graphing Utility.

The graph of a parabola is

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Most popular questions from this chapter

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

6x2+3y2-12x+6y=0

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

4x2+12xy+9y2-x-y=0

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y2=8x

Transform the equation r=6cos(胃)from polar coordinate to rectangular coordinate.

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