Question $1.$ Let $Obe$ the origin and $lbe$ a fixed lien $in$ plane. Let $ebe$ a fixed

positive numbers. Let a curve $Cbe$ the set $of$ all points $Pin$ the plane such

that

$\frac{|OP|}{|Pl|}=e$

That $is,$ the ratio $of$ the distance from $Oto$ the distance from $lise.$

$(a)$ Show that $Cisan$ ellipse $ife>1,$ a hyperbola and a parabola $if$

$e=1.$

$(b)$ Find the polar equation $ofC.$