P and Q are the points on the ellipse 3 x 2 + 4 y 2 = 12 with eccentric angles α and β respectively and whose foci are at S and S ′ . If PS and QS ′ are parallel then t a n 2 β t a n 2 α can be

Question

P and Q are the points on the ellipse 3 x 2 + 4 y 2 = 12 with eccentric angles α and β respectively and whose foci are at S and S ′ . If PS and QS ′ are parallel then t a n 2 β ​ t a n 2 α ​ ​ can be equal to

TestHub · Accepted Answer

Let P and Q be ( a cos α , b sin α ) and ( a cos β , b sin β ) since PS and Q S ′ parallel ⇒ a c o s β + ae b s i n β ​ = a c o s α − ae b s i n α ​ on solving sin ( α − β ) + e ( sin α + sin β ) = 0 cos 2 α − β ​ ( sin 2 α − β ​ + e sin 2 α + β ​ ) = 0 2 α − β ​ = 2 π ​ tan 2 β ​ tan 2 α ​ ​ = 1 + e 1 − e ​ 1 − e 1 + e ​

Mathematics - Ellipse Question with Solution | TestHub

Options:(select one or more)

Doubts & Discussion