Find the two horizontal and two vertical tangent lines of the equation x^2+xy+y^2=9.

Question

Mathematics

Leon Villegas

21 May, 04:13

Find the two horizontal and two vertical tangent lines of the equation x^2+xy+y^2=9.

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Answers (1)

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Aliyah Newton · Answer 1

Differentiating w. r. t y,

We get,

2 x (d x/d y) + y (d x/d y) + x + 2 y = 0

Put

d x/d y = 0

The equation becomes:

x=2 y

substituting into main equation

We, get

3 y^2 = 9

y = √3

x = ± 2√3