If the line x+2y+4=0 cutting the ellipse x2a2+y2b2=1 in points whose eccentric angles are 30∘ and 60∘ subtends a right angle at the origin then its equation is
x216+y24=1
slope of line =ba(sin 60∘−sin 30∘cos 60∘−cos 30∘)=−ba=−12
Homogenizing the ellipse with x+2y−4=0
x24b2+y2b2=(x+2y−4)2⇒1b2(x24+y2)=x2+4y2+4xy16
Coefficient of x2+coefficient of y2=0
14b2−116+1b2−416=0⇒b2=4,b=2⇒a=4Ellipse is x216+y24=1