Question

The equation of the tangent to $y=be^{-x/a}$ at the point where it crosses the Y axis is}

• A. $x+y=ab$
• B. $\frac{x}{a}+\frac{y}{b}=1$
• C. $ax+by=1$
• D. $x+y=a+b$

Hint:

Tangent crossing the Y-axis always has the form $y - y_0 = m(x)$.

Answer 1

The Correct Option is B

Step 1: Concept
At the Y-axis crossing, $x = 0$.

Step 2: Analysis
When $x=0$, $y = be^0 = b$. Point of contact is $(0, b)$.
Slope $dy/dx = b(-1/a)e^{-x/a}$. At $x=0$, $m = -b/a$.

Step 3: Calculation
Equation of tangent: $y - b = -\frac{b}{a}(x - 0)$
$ay - ab = -bx \implies bx + ay = ab$.
Dividing by $ab$: $\frac{x}{a} + \frac{y}{b} = 1$.

Step 4: Conclusion
Hence, the tangent equation is $x/a + y/b = 1$. Final Answer: (B)