IIT JEE , AIEEE Forum - Mathematics , Algebra

shubham.123

let z =1-t+i

t^2 +t+2 t is real parametre the locus of z is

seraphic

is it a parabola?

Greatdreams

No I think its a hyperbola

x + i y = z = 1 - t + i

(t² + t + 1)

So

we have to eliminate t

x = 1 - t

Hence t = 1 - x

y =

(t² + t +1)

y² = t² + t + 1

or y ² = (1 - x) ² + 1- x + 2 = 1 - 2x + x² + 3 - x = x² + 4 - 3x

or y² = (x - 3/2 )²+ 7/4

So y² - (x - 3/2)² = 7/4

which represents a hyperbola .

coolriya

the locus is a hyperbola......

but great dreams ..

re : u've solved for :

x + i y = z = 1 - t + i^{[ ]}

(t2 + t + 1)

but the q is :let z =1-t+i ^{[ ]}

t^2 +t+2

neways my ans is also the same........

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