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The length of subtangent to the curve x^...

The length of subtangent to the curve `x^2 + xy + y^2=7` at the point `(1, -3)` is

A

3

B

5

C

`3/5`

D

15

Text Solution

Verified by Experts

The correct Answer is:
D
Given curve is `x^(2)+xy+y^(2)=7`
`implies2x+x (dy)/(dx)+y+2y(dy)/(dx)=0`
`implies(dy)/(dx)=-((2x+y))/(x+2y)`
At `(1,-3), ((dy)/(dx))_((1,-3))=(-(2-3))/((1-6))=-1/5`
`:.` Length of subtangent `y/((dy)/(dx))=(-3)/(1/(-5))=15`
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