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Question

One focus of a hyperbola is (3,0) and its corresponding directrix is 4x−3y−3=0. If its e=54 then one vertex is :

A
(35,115)
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B
(115,35)
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C
(75,45)
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D
(45,75)
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Solution

The correct option is A (115,35)
Distance from focus to directrix is a (1e+e)
a(5445)=4(3)35
a(920)=95
a=4
Given focus slope of axis is (34) travelling along axis parametric equation of point are (3+r(45));0+r(35)
r=aea=a(14)=1
Vertex =(345,35)=(115,35)

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