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Chapter 11: Q.125 (page 1119)

In the following exercises, (a) write the equation in standard form and (b)graph4x2+25y2-24x-64=0

Short Answer

Expert verified

The required standard equation is (x-3)225+y24=1

Step by step solution

01

Part(a): Step 1, Given the information   

The given equation of the ellipse is4x2+25y2-24x-64=0

02

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

4x2+25y2-24x-64=04x2-24x+25y2-64=0(paring)4(x2-6x)+25y2-64=0(common)4(x2-2*3x+9-9)+25y2-64=04(x-3)2-36+25y2-64=04(x-3)2+25y2=100(x-3)225+y24=1

03

Part(a): Step 3. Conclusion 

Hence, the required standard equation of the ellipse is (x-3)225+y24=1

04

Part (b): Step 1, Given the information   

The given equation is(x-3)225+y24=1

05

Part (b): Step 2. draw  a graph  

The standard equation of the ellipse is (x-3)225+y24=1

Whose center is 3,0and 25>4The major axis is horizontal

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