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Chapter 10: Q. 34 (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 2,4; directrix the line x = -4

Short Answer

Expert verified

The equation of the parabola is3y2-12y-4x+11=0.

Step by step solution

01

Step 1.  Given information .

Consider the given vertex and directrix .

02

Step 2. Equation of parabola used.

A parabola whose focus is at 2,4and directrix is the horizontal line x = -4 has its vertex -1,2.

The equation of parabola is y-k2=4ax-h.

Substitute the values of focus and vertex in the equation of parabola to find a.

y-k2=4ax-h4-22=4a2+1a=13

Further simplify.

y-22=43x+1

03

Step 3. Plot the graph.

The graph of the given equation 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.

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