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Find the focus and the directrix of the parabola y 2 = 2a(x – 4a) and give the length of the latus rectum

Find the focus and the directrix of the parabola y2 = 2a(x – 4a) and give the length of the latus rectum

Grade:12

2 Answers

Aditya Gupta
2081 Points
4 years ago
eqn is y2 = 4(a/2)(x – 4a)= 4(a/2)X, where X= x – 4a
now obviously focus, directrix and latus rectum of y^2= 4bX are (b, 0), X= – b and 4b.
so, in our original coordinate system, focus is (4a + a/2, 0), directrix is x – 4a= – a/2 or x= 7a/2 and latus rectum= 4a/2 (as it is a length).
so, focus: (9a/2, 0)
directrix: 2x= 7a
LR= 2a
kindly approve :)
Sai Soumya
99 Points
4 years ago
The required answer is according to the given equation is
FOCUS : (9a/2,0)
DIRECTRIX : X=7a/2
LENGTH OF LATUS RECTUM : 2a

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