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Chapter 11: Q.126 (page 1119)

In the following exercises, (a) write the equation in standard form and (b)graph 9x2+4y2+56y+160=0

Short Answer

Expert verified

The required standard equation isx24+y+729=1

Step by step solution

01

Part(a): Step 1, Given the information 

The given equation of the ellipse is,9x2+4y2+56y+160=0

02

Part(a):  Step 2. Convert the equation into standard form  

9x2+4y2+56y+160=09x2+4(y2+14y)+160=09x2+4(y2+2*7y+49-49)+160=09x2+4y+72-196+160=09x2+4y+72-36=09x2+4y+72=36x24+y+729=1

03

Part(a): Step 3. Conclusion  

Hence, the required standard equation of the ellipse is x24+y+729=1x24+y+729=1

04

Part (b): Step 1, Given the information   

The given equation isx24+y+729=1

05

Part (b): Step 2. draw  a graph 

The standard equation of the ellipse is x24+y+729=1

Whose center is 0,-7and 4<9
The major axis is vertical

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