If a hyperbola passes through the point P (√2,√3) and has foci (±2,0), then the tangent to this hyperbola at P also passes through the point
A
(3√2,3√3).
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
(2√2,3√3).
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
(√2,√3).
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
(−√2,−√3).
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is B(2√2,3√3). Let the equation of hyperbola be x2a2−y2b2=1 ∴ae=2⇒a2e2=4⇒a2+b2=4⇒b2=4−a2∴x2a2−y24−a2=1Since,(√2,√3)lieonhyperbola.∴2a2−34−a2=1⇒8−2a2−3a2=a2(4−a2)⇒8−5a2=4a2−a4⇒a4−9a2+8=0⇒(a2−8)(a2−1)=0⇒a2=8,a2=1
Now equation of hyperbola is x21−y23=1 ∴ equation of tangent at (√2,√3)isgivenby√2x−√3y3=1⇒√2x−y√3=1
which passes through the point (2√2,3√3).