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Question

Find the eccentricity, foci, centre, length of latus rectum vertices and the equation to the directrices of the hyperbola.
(a) 9x216y2+72x32y16=0
(b) 4x25y216x+10y+31=0
(c) 5x24y2+20x+8y4=0
(d) 4(y+3)29(x2)2=1
(e) 4x29y28x32=0.

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Solution

(a) e=54, latus rectum =92,c=(4,1),foci(1,1),(9,1),Vertices=(0,1)(8,5)Directrices 5x+36=0,5x+4=0.

(b) e=32,latus rectrum=5,c=(2,1), foci=(2,4),(2,2),vertices(2,3),(2,1),directrices3y7=0,3y+1=0.

(c) e=32,latus rectum=5,foci(1,1)(5,1),centre=(2,1), vertices(0,1),(4,1),directrices3x+2=0,3x+10=0.

(d) e=133,foci=(2,3±12133),latus rectum=49,vertices(2,3,±12),directrices y=3±223.

(e) e=133,centre=(1,0),foci=(1±13,0),latus rectum=83,vertices(4,0),(2,0),directrices x=1±913.

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