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BITSAT2020MathematicsApplication of DerivativesActual

The equation of the tangent to the curve y=b e^ -x/a at the point where it crosses the y -axis is

Options

  1. Ax a - y b =1
  2. Ba x+b y=1
  3. Ca x-b y=1
  4. Dx a + y b =1

Correct answer

D. x a + y b =1

Step-by-step solution

y=b e^ -x / a meets the y -axis at (0, b) . Again, d y d x =b e^ -x / a (- 1 a ) At (0, b), d y d x =b e⁰ (- 1 a )=- b a Therefore, required tangent is y-b=- b a (x-0) or x a + y b =1

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