algebra

2)
parabola

ellipse

hyperbola ??

since here a=b
so \left|a \right|=\left|b \right|=\left|\bar{b} \right|=\left|\bar{a} \right|
and since
the given eq is

2\left(\frac{\left|\bar{b}z+b\bar{z} +c\right|}{2\left|b \right|} \right)=\alpha \left|z-z_{1} \right|

\left(\frac{\left|\bar{b}z+b\bar{z} +c\right|}{2\left|b \right|} \right)=distance of z from line \bar{b}z+b\bar{z} +c

and \left|z-z_{1} \right| is distance of point z from z₁

hence we can clearly see here \frac{2}{\alpha } is the eccentricity of conic

and z₁ is teh focus and \bar{b}z+b\bar{z}+c=0 is the directrix

now e=\frac{2}{\alpha }

wen \alpha =2 it is a parabola

wen \alpha >2 it is an ellipse

wen \alpha <2 it is a hyperbola

Where are these qns from? BTW, I've just seen a beautiful soln to #1 on Mathlinks - http://www.mathlinks.ro/viewtopic.php?t=329319

Do read it.

Someone's posted Q3 is disguised form asking what is max of sin θ + sin 2θ

yup i saw u posted der :P

check this for another way

for 1st q

http://www.mathlinks.ro/viewtopic.php?p=1762870#1762870

it turns out to be Vandermonde's Convulution identity

got to know abt it today only [3]

btw this aint related to jee by miles