Let axes of ellipse be coordinate axes, S and S′ be foci, B and B′ are the endpoints of the minor axis. If sin(∠SBS′)=45 and area of SBS′B′ is 20 sq. unit, then the equation of ellipse is
A
x220+y216=1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
x218+y213=1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
x225+y216=1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
x225+y220=1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution
The correct option is Dx225+y220=1 Given, area of SBS′B′=20 ⇒12(2ae)×(2b)=20⇒aeb=10⇒a2e2=100b2⋯(1)
And sinθ=45⇒tanθ=43⇒43=2tanθ/21−tan2θ/2⇒2tan2θ2+3tanθ2−2=0⇒(2tanθ2−1)(tanθ2+2)=0⇒tanθ2=12(∵tanθ2≠−2,θ∈(0,π))⇒aeb=12⋯(2)