Question
Question: The equation of the tangent to the curve \(y = be^{- x/a}\) at the point where it crosses y-axis is...
The equation of the tangent to the curve y=be−x/a at the point where it crosses y-axis is
A
ax+by=1
B
ax−by=1
C
ax−by=1
D
ax+by=1
Answer
ax+by=1
Explanation
Solution
Curve is y=be−x/a
Since the curve crosses y-axis (i.e., x=0) ∴ y=b
Now dxdy=a−be−x/a. At point (0, b), (dxdy)(0,b)=a−b
∴ Equation of tangent is y−b=a−b(x−0) ⇒ ax+by=1.