1. EJERCICIO UNIDAD TRES HIPÉRBOLAS
Ejercicio: (𝒙 − 𝟒)𝟐
+ (𝒚 − 𝟓)𝟐
=
𝟕
𝟑
Coordenadas del centro:
(𝒙 − 𝒉)𝟐
𝒂𝟐
+
(𝒚 − 𝒌)𝟐
𝒃𝟐
= 𝟏
(𝒙 − 𝟒)𝟐
+ (𝒚 − 𝟓)𝟐
=
𝟕
𝟑
(𝒙 − 𝟒)𝟐
𝟕
𝟑
𝒂𝟐
+
(𝒚 − 𝟓)𝟐
𝟕
𝟑
𝒃𝟐
= 𝟏
Centro= 𝐶(ℎ, 𝑘) = 𝐶(4,5)
𝒂𝟐
=
𝟕
𝟑
𝒃𝟐
=
𝟕
𝟑
𝑎2
=
𝟕
𝟑
√𝑎2 = √
𝟕
𝟑
𝑎 = 1,527
√𝑏2 = √
𝟕
𝟑
𝑏 = 1,527
Foco= 𝑐
𝑐2
= 𝑎2
− 𝑏2
𝑐2
=
7
3
−
7
3

2. 𝑐2
= 0
√𝑐2 = √0
𝑐 = 0
Excentricidad= 𝑒 =
𝑐
𝑎
𝑒 =
0
7
3
= 0
Lado Recto= 𝐿𝑅 =
2𝑏2
𝑎
𝐿𝑅 =
2 ∗ (
7
3
)2
1,527
= 0.5893
0.5893
2
= 0.2946
𝑉1 = 2.4724
𝑉2 = 5.5275
Gráfica: