Question

The chord AC of parabola y^2=4x subtends 90° angle at points B and D on parabola.Of A,B,C, and D are represented by t1,t2,t3,t4 then

Answer 1

|t2t4-t1t3| =?

Answer 2

@ganeshie8

Answer 3

Could you draw the parabola and label the points/lengths ?

Answer 4

I just got two equations which are:-
(t1+t2)(t2+t3)=-4
(t1+t4)(t3+t4)=-4

Answer 5

I don't understand the question; The way you have phrased it is very confusing

Answer 6

Instead of the word "Of" in the question it is "if".

Answer 7

Sorry I don't get why you want to label the points by two names. Something seems to be wrong

Answer 8

It would help if you take a screenshot of entire question and attach

Answer 9

t1,t2,t3,t4 are the parameters of A,B,C AND D.

Answer 10

Do you mean t1, t2, t3, t4 are the "position vectors" of the points A, B, C, D ?

Answer 11

Like the point A is (at1^2, 2at1) , we have assigned it a parametric term (t1) and likwise it is for the rest of them.

Answer 12

Did you get it?

Answer 13

y^2 = 4x


parametric form would be (t^2, 2t)

Answer 14

Are you saying

A = (t1^2, 2t1)
B = (t2^2, 2t2)
C = (t3^2, 2t3)
D = (t4^2, 2t4)

?

Answer 15

Yup that's how he assigned the paramaters.

Answer 16

I'm guessing you would find the gradients of AB, AD, BC and CD

Answer 17

She*
And yes ganeshie sir that's what i mean.

Answer 18

then you should end up with the equations
(t1+t2)(t2+t3) = -1
(t1+t4)(t4+t3) = -1

right ?

Answer 19

Why so?
We have a slope of any chord to be 2/t1+t2 for a parabola.

Answer 20

okay -4 on the right hand side
lets see where to go from here

Answer 21

We didn't use the value of a of parabola in coming to this conclusion though.I think second equation must result from use of that.

Answer 22

@parthkohli

Answer 23

@thomas5267

Answer 24

I don't even understand the question. I am too tired now anyway.