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Question

The sum of intercepts on coordinate axes made by tangent to the curve x+y=a is


A

a

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B

2a

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C

2a

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D

None of these

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Solution

The correct option is A

a


Explanation for the correct option:

Find the required sum.

Given curve: x+y=a

On differentiating w.r.t x, we get

12x+12ydxdy=0

dxdy=-yx ( slope of tangent)

To find points,

Let x=c

y=(ac)2

So, equation of tangent ,

Y-a-c2=-yxX-cY-a-c2x-c=-yxY-a-c2X-c=-a-c2c[x=c&y=a-c2]

Y-a-c2X-c=c-ac ….(i)


For Intercept of x,

putY=0 in equation (i) we get,

X=ac ….(ii)
For intercept of y,

putX=0 in equation (i) we get,

Y=aac …(iii)

Sum of both Intercepts (ii)+(iii)

ac+a-ac=a

Hence, option (A) is the correct answer.


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