x？ /( 144/ 16)+y？ /( 144/9)= 1

x？ /( 12/4)? +y？ /( 12/3)? = 1

x？ /(3? )+y？ /(4? )= 1

X? /(b？ )+y？ /(a？ )= 1

Major axis =a minor axis =b focal length =2c c? =a？ -B? Focus f 1, 2 = (0, c) Eccentricity = c/a.

Known major axis =4 minor axis =3 focal length =2√7 focal point F 1, 2 = (0, √7) eccentricity =√7/4.

Major axis =8 minor axis =6

2,4x2+9Y2 =1Substitute into the standard equation x? /( 1/2)? +y？ /( 1/3)? = 1

Major axis = 1/2 minor axis = 1/3 focal length =√5/3 focal point F 1, 2 = (√ 5/6,0) eccentricity =√5/3.

Major axis = 1 minor axis =2/3

3, x2/25+y2/ 16= 1 into the standard equation x? /(5? )+y？ /(4? )= 1

The solution is the same as 2,

4, x2/5+y2/9= 1 into the standard equation x? /(√5)? +y？ /(3? )= 1

The solution is the same as 1.

Write the standard equation.

First, the focal points of the long axis 6 and the short axis 4 are on the Y axis. Answer? =(6/2)? =9 b？ =(4/2)? =4

x？ /4+y？ /9= 1

Second, the sum of the distances from a moving point to two small points 4 focal length 2 focal point is on the X axis.

2a=4 a？ =4 2c=2 c= 1 c？ =a？ -B? b？ =4- 1=3

x？ /4+y？ /3= 1

Thirdly, the eccentricity of the short semi-axle 8 is 3/5, and the focus is on the Y-axis.

b = 8°c/a = 3/5°c？ =a？ -B? 9a？ /25=a？ -8? Answer? = 100

x？ /64+y？ / 100= 1

IV. Sum of major and minor axes 16 focal length 8

2a+2b= 16 2c=8 a+b=8 c？ =a？ -B? =(a+b)(a-b) 4？ =8(a-b) a-b=2

The solution is a=5 b=3.

Standard equation x? /25+y？ /9= 1

. Or x? /9+y？ /25= 1