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focus of parabola is (2,3) and directrix is 4x-3y+6=0.find length of latus rectum.

focus of parabola is (2,3) and directrix is 4x-3y+6=0.find length of latus rectum.

Grade:12th pass

1 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
5 years ago
length of the latus rectum is 4p
where p is the distance from the focus to the vertex
now distance from focus to vertex = distance from vertex to directrix = p
and as focus and vertex lie in line perlendicular to directrix
distance from focus to directrix = 2p
in this case
2p = |4\times2 - 3\times3 + 6|/\sqrt{4^2+3^2} = 5/5 = 1
so
answer = 4p = 2

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