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Lesson: 5.4 Hyperbola 双曲线
5.4 Hyperbola 双曲线

(1)

Find the centre, vertex, axis of symmetry, transverse semi-axis, conjugate semi-axis, eccentricity, focus, directrix, length of latus rectum and asymptotes for the following hyperbola and sketch the graph.

(a) 9x – y = 9

(b) y – 4x = 1

(c) 4x – 9y – 16x – 18y – 29 = 0

(2)

Find the equation of the hyperbola with center at (-7, -2), transverse axis parallel to the x-axis, eccentricity , latus rectum .

(3)

Find the equation of the hyperbola with asymptotes 2x – y = 0, 2x + y – 4 = 0 and passes through the point (6, 10).

(2x – y) (2x + y – 4) = 36
(4)

Find the equation of the hyperbolic with center (3, -6), conjugate axis parallel to the x-axis, distance between foci , distance between directrices .

(5)

Given that P is on the right side of the hyperbola, its distance to the right directrix is , calculate the distance of P to the left focus.

11
(6)

If the hyperbola and circle don’t have intersection point, find the range of the real value k.

or
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