The tangent at a point P on the hyperbola x2a2−y2b2=1 meets one of the directrix in F. IF PF subtends an angle θ at the corresponding focus, then θ equals :
A
π4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
π2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
3π4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
π
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is Dπ2 Let the directrix be x=ae and focus be S(ae,0). Let P(secθ,btanθ) by any point on the curve.
Equation of tangent at P is xsecθa−ytanθb=1.
Let F be the inetrsection point of tangent and the directrix, then F=(ae,b(secθ−e)etanθ)