Gabarito apostila conicas

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Gabarito - Apostila:Cônicas 
Circunferência 
1. a) �� � 4�� � �� � 3�� 
 25;		�� � �� � 8� � 6� 
 0 
b)	�� � 5�� � �� � 12�� 
 9;		�� � �� � 10� � 24� � 160 
 0 
2. �� � �� � 2� � 4� � 8 
 0 
3. a) ��3,4�, � 
 4 b)� �0,� ��� , � 
�
� 
4. ��1,�3�, � 
 5; ���, ����� 
 3; � !"�#!�$� 	��	� ���	é	8&. �. 
5. �� � 3�� � �� � 4�� 
 17 
6. �� � 1�� � �� � 5�� 
 26 
Parábola 
1. a) )�0,1�; � 
 �1; b) )��2,0�; � 
 2; c) ) �*+ , 0� ; � 
 �
*
+ 
 
 
 
2. a) �� 
 20�; b) �� 
 �8�; c) �� 
 2�; d) �� 
 8�; e) �� � 8� 
 0 f) 
�� 
 �12�. 
 
 
 
3. �� � � 
 0 
4. a) " 
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, , 0� , � 
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,; b) " 
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, , 0� , � 
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,; 
c)" 
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-
,.� , � 
 �
-
,. 
 
 
 
5. Gráfico: 
 
Elipse 
1. a) /�0,05�; )�0,0√21�; 	� 
 √�-� ; b) /�04,0�; )�0√7, 0�; 	� 
√2
, 
 
 
2. a) 9�� � 25�� 
 225; b)2�� � �� � 50 
 0; c)34-5 �
64
2 
 1 
 
 
 
3. 37
4
* �
674
, 
 1; 	��3, �1�;	/-�0, �1�, /��6, �1�; � 
√�
� 
 
4. � 
 5, 8 
 3, )�04,0�; � 
 ,� 
 
5. /�0,04�; )�0,0√7�; 	� 
 √2, 
 
6. �39,�
4
�5 �
�69��4
�2 
 1 
 
Hipérbole 
1. a) /�02,0�, ):0√13, 0;, � 
 √-�� , � 
 0
�
��; 
b) /�, 0�, )�, 0�, � 
 √-�� , � 
 0
�
�� 
c) /�04,0�, )�05,0�, � 
 �, , � 
 0
�
, � 
d) /:02√2, 0;, ):02√3, 0;, � 
 √5� , � 
 0
√�
� � 
e) /�, 0�, )�0,0�, � 
 √-�� , � 
 0� 
 
 
2. a) 16�� � 9�� � 144 
 0 
b) 4�� � 5�� � 20 
 0 
c) �� � 3�� � 75 
 0 
d) 4�� � 7�� � 28 
 0 
 
3. � 
 02, 8 
 04, � 
 2√5, � 
 √5, � 
 0 -� � 
 
4. 37
4
, �
674
* 
 1, ��1, �2�, /-��1,�2�, /��3, �2�, � 
√-�
� 
 
5. 3
4
-5 �
64
* 
 1;	
64
* �
34
-5 
 1 
 
6. �6<��
4
, �
�39��4
* 
 1; 	4�
� � 9�� � 16� � 36� � 16 
 0 
 
 
Superfícies Quádricas 
1. a) 34, �
64
* �
=4
- 
 1, elipsóide. 
b) 34- �
64
, �
=4
* 
 1, hiperbolóide de uma folha. 
c) 34- �
64
, �
=4
* 
 1, hiperbolóide de duas folhas. 
d) 34�5 �
64
�5 �
=4
�5 
 1, superfície esférica. 
e) 34- �
64
- 
 9>, parabolóide circular. 
f) 34, �
64
, �
=4
� 
 1, hiperbolóide de uma folha. 
Coordenadas Polares 
1. a) ��3,0� 
b) ��1,�1� 
c) �2, �2√3� 
d) �0,2� 
e) ��√2,√2� 
f) �� √�� ,
-
�� 
2. a) �2, --?5 � b)��2,
�?
� �