Question

obtain the parametric equations of y^2 = 4x. the answers are x= 4/t^2 and y=4/t. why is this??

Answer 1

This is because t is the parameter since we write parametric form in terms of r he took in terms of t

Answer 2

so..

Answer 3

okay..

Answer 4

aah this is

Answer 5

well do this find y(t)
it well abear that
\[\left( \frac{ 4 }{ t } \right)^2=4\left( \frac{ 4 }{ t^2}\right)\]
\[\frac{ 16 }{ t^2 }=\frac{ 16 }{ t^2 }\rightarrow L.H.S=R.H.S\]

Answer 6

what is LHS??

Answer 7

left hand side

Answer 8

so is it always that we have to assume that y is t?

Answer 9

no , assume f(x) = y
and find f(t).

Answer 10

im so sorry i still find it so difficult. my prof wasn't able to explained this topic to us.. so for example x^2 + 2x - y = 0?

Answer 11

is x & y are still defind as you mintioned in the Q ?

Answer 12

it wasn't mentioned.

Answer 13

\[x^2 +2x-y=0\rightarrow y=x^2+2x\]
assume f(x)=y
\[f(x)=x^2+2x\]
to check find f(t)
if \[x=\frac{ 4 }{ t^2 } and \rightarrow y=\frac{ 4 }{ t } \]
\[\frac{ 4 }{ t }=\left( \frac{ 4 }{ t^2 } \right)^2 + 2\left( \frac{ 4 }{ t} \right)\]

Answer 14

x^2 + 2x - y = 0, the answers are x= t-2 and y = t(t-2) the answers are mention in the book

Answer 15

but if you want to find the root of
x^2 + 2x - y = 0?
y=x^2+2x you must have Points satisfy the equation
so if you have point use Use the derivation

Answer 16

so you wana have to check the answer or prove it !

Answer 17

derivation. so its 2x + 2

Answer 18

yes .

Answer 19

aah i cant get x= t-2. why is this happeniing to me