I know this is a long solution , but I think you will get it completely.
Correct in order to lessen Ur time u can remember that length of focal cord with point (at1,2at1) =a(t+1/t)^2
This reduces this prob to few line
And length of focal chord making angle theta with x axis is 4acosec^2theta
@Gaurav_Singh11 how did you get c =1+t^2. What is t, parameter?
Yes t is parameter
How is the length 1+t^2
@Gaurav_Deshpande , focal distance of any point on the parabola y^2 =4ax is a + at^2. This is the reason.
@Gaurav_Singh11 what did you do in next step?
I am not clear which step you are asking?
Where you have taken C=5 then c =5/4
I have solved for the value of c on right side and then for Finding the value of t have put into the equation
C = 1+ t^2
On the right is there some formula for focal lengths?
AC is a focal chord .So, we can write this equation from it.
I'm not getting how did you write that equation. @Gaurav_Singh11 you can edit the before post if there is 5min limit
@Gaurav_Deshpande , have you studied Properties of focal chord? It is from there , if you want notes of it I can share
I hope you understand it , you can ask if you have more doubts.
Thanks a lot