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

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

Grade:12

4 Answers

Vikas TU
14149 Points
5 years ago
Dear student 
Please specify what is p here ? Is it a constant or some variable. 
You can also attach an image 
We will help you
Good luck
Aditya Gupta
2086 Points
5 years ago
vikas’ ans is the crappiest ans here. the correct ans is as follows and the ques is perfectly fine.
let p= 2a.
so, eqn is y2 = 4a(x – 8a)= 4aX, where X= x – 8a
now obviously focus, directrix and latus rectum of y^2= 4aX are (a, 0), X= – a and 4a.
so, in our original coordinate system, focus is (8a + a, 0), directrix is x – 8a= – a or x= 7a and latus rectum= 4a (as it is a length).
so, focus: (9p/2, 0)
directrix: 2x= 7p
LR= 2p
kindly approve :)
Samuel William
25 Points
5 years ago
@Viska Tu
In my country, we use p instead of a. So the question is to find the focus, directrix and latus rectum of the parabola;
y2 = 2a (x – 4a)
 
Samuel William
25 Points
5 years ago
@Aditya
Thanks for your answer. But how do I solve the problem if the parabola was; y2 = 2a (x – 4a).
thank you.

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