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Chapter 11: Q.123 (page 1119)

In the following exercises, (a) write the equation in standard form and (b)graph
25x2+9y2-100x-54y-44=0

Short Answer

Expert verified

The required standard equation is(x-2)29+(y-3)225=1

Step by step solution

01

Part(a): Step 1, Given the information 

The given equation of the ellipse is25x2+9y2-100x-54y-44=0

02

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

Here,25x2+9y2-100x-54y-44=025x2-100x+9y2-54y-44=0(pairing)25(x2-4x)+9(y2-6y)-44=0(takingcommon)25(x2-2*2x+4-4)+9(y2-2*3y+9-9)-44=025(x-2)2-25*4+9(y-3)2-9*9-44=025(x-2)2-100+9(y-3)2-81-44=025(x-2)2+9(y-3)2-225=0(x-2)29+(y-3)225=1

03

Part(a): Step 3. Conclusion

Hence, the required standard equation of the ellipse is (x-2)29+(y-3)225=1

04

Part (b):Step 1, Given the information 

The given equation is(x-2)29+(y-3)225=1

05

Part (b): Step 2. draw  a graph

The standard equation of the ellipse is (x-2)29+(y-3)225=1

Whose center is 2,3and 9<25, The major axis is vertical

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