The equation of the tangent to the curve (xa)n+(yb)n=2 at (a,b) is
A
xa+yb=2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
xa+yb=12
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
xb−ya=2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
ax+by=2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is Axa+yb=2 The given curve is (xa)n+(yb)n=2 ⇒n(xa)n−1⋅1a+n(yb)n−1⋅1bdydx=0 ⇒dydx=−ba(xa)n−1(yb)n−1 At (a,b)dydx=−ba(1)n−1(1)n−1=−ba Therefore, the tangent at (a,b) is y−b=−ba(x−a) ⇒ay−ab=−bx+ab ⇒bx+ay=2ab ⇒xa+yb=2.