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Chapter 8: Q9. (page 423)

Write an equation for the parabola having focus 3,8 and directrix y=4. Then draw the graph.

Short Answer

Expert verified

The required equation of the parabola isy=18x-32+6.

Step by step solution

01

Step 1. Write down the given information.

The given parabola has focus 3,8 and directrix y=4.

02

Step 2. Concept used.

If Px,y be any point on parabola having focus f1,f2 and directrix y=athen:

Distance of point Px,y from focus f1,f2= Distance of point Px,y fromx,a

03

Step 3. Calculation.

Since the given parabola has focus 3,8and directrix y=4. Therefore, apply the concept stated above,

Distance of point Px,y from focus 3,8= Distance of point Px,y from x,4

x鈭�32+y鈭�82=x鈭�x2+y鈭�42x鈭�32+y鈭�82=x鈭�x2+y鈭�42....Squaringx鈭�32=y鈭�42鈭�y鈭�82x鈭�32=2y鈭�124x鈭�32=8y鈭�48y=18x鈭�32+6

Hence, y=18x-32+6 is the required equation of the parabola.

04

Step 4. Sketch the graph of the parabola.

The graph of the parabola y=18x-32+6 is shown below.

05

Step 5. Conclusion.

The required equation of the parabola is y=18x-32+6.

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