The slope of the tangent line to a curve at any point (x, y) on the curve is x divided by y. What is the equation of the curve if (3, 1) is a point on the curve?

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The slope of the tangent line to a curve at any point (x, y) on the curve is x divided by y. What is the equation of the curve if (3, 1) is a point on the curve?

Answer 1 · 2015-06-30 03:34:15

slope = x/y = 3/1 = 3

so the equation of the tangent at the point (3,1) is
y-1 = 3(x-3)
y = 3x -8 or 3x - y - 8 = 0

Answer 2 · 2015-06-30 04:26:02

y' = x/y
you can recognize that as an hyperbola

x^2-y^2 = a^2
since (3,1) is on the curve,
9-1 = a^2

x^2-y^2 = 8

Answer 3 · 2015-06-30 11:23:11

Maybe I should become a politician.
Never actually answer the question, rather give an answer to some other question.
Thanks for the catch Steve, that is two for one evening, I should get more sleep.

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The slope of the tangent line to a curve at any point (x, y) on the curve is x divided by y. What is the equation of the curve if (3, 1) is a point on the curve?

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