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Question

The equation of the tangent to curve y=be-xa at the point where it crosses y – axis is


A

ax+by=1

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B

ax-by=1

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C

xayb=1

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D

xa+yb=1

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Solution

The correct option is D

xa+yb=1


Explanation for the correct answer:

Step 1: Find the first order derivative of the equation of the curve

Given equation of curve is y=be-xa

Differentiating with respect to x we get

dydx=b×-1a×e-xa

dydx=-ba×e-xa

Step 2: Find the slope of the tangent at required point

Let P(0,y1) be the point where tangent to curve crosses y-axis .

y1=be0

y1=b

So, the pointP is(0,b)

The first order derivative at a point gives the slope of the tangent at the given point

dydx0,b=m=-ba×e0

m=-ba

Slope of tangent at P(0,b) is -ba

Step3: Write the equation of the tangent using slope point form

Equation of tangent through P(0,b) is

yb=-ba(x0)bx+ay=abxa+yb=1

Hence, the correct answer is option (D).


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