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Question

Equation of one of the latus rectum of the hyperbola (10x5)2+(10y2)2=9(3x+4y7)2 is 


A
30x+40y23=0
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B
40x+30y23=0
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C
30x+40y+23=0
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D
40x+30y+23=0
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Solution

The correct option is A 30x+40y23=0
Given, hyperbola is
(10x5)2+(10y2)2=9(3x+4y7)2

100[(x12)2+(y15)2]=9(3x+4y7)2

(x12)2+(y15)2=94(3x+4y725)2
 
Which represents hyperbola having one focus S(12,15) and directrix equation as 3x+4y7=0
Let equation of latus rectum be 3x+4y+λ=0
As it passes through (12,15)
λ=2310

Hence, equation of the latus rectum is 30x+40y23=0
 

Mathematics

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