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Find the (i) lengths of axes, (ii) coordinates of the vertices, (iii) coordinates of the foci, (iv) eccentricity, and (v) length of the latus rectum of the hyperbola. Horizontal Hyperbola:

For general form of Hyperbola: 

x2/a2 – y2/b2 = 1 ……..(1) 

Vertical Hyperbola:

For general form of Hyperbola:

y2/a– x2/b= 1 ……..(2) 

5y2 – 9x2 = 36

1 Answer

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Divide each side by 36, we get

y2/(36/5) – x2/4 = 1

Which is of the form y2/a2 – x2/b2 = 1

On comparing given equation with (2), we get

a = 6/√5 and b = 2

Then,

c2 = a2 + b2

c2 = 36/5 + 4 = 56/5

or c = 2√(14/5)

Now,

(i) Lengths of the axes:

Length of Transverse axis = 2a = 12/√5 units

Length of Conjugate axis = 2b = 4 units

(ii) Coordinates of the vertices: (0, ±a) = (0, ±6/√5)

(iii) Coordinates of the foci: (0, ±c) = (0, ±2√(14/5))

(iv) Eccentricity: e = c/a = √14/3

(v) Length of the latus rectum: 2b2/a = 4√5/3 units

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