Question

The slope of the tangent to a curve at any point (x, y) on the curve is -x/y. Find the equation of the curve if the point (2, −2) is on the curve.

Answer 1

not sure how to do this one

Answer 2

what do you know about the relation between `slope of tangent line` and `first derivative` ?

Answer 3

well the first derivative represents the slope of the tangent line on any point of the function you derive

Answer 4

You're given that the `slope of tangent line` equals -x/y,
so setup an equation using that info

Answer 5

i thought that -x/y was the derivative

Answer 6

Yes
\[\dfrac{dy}{dx}=\dfrac{-x}{y}\]

Answer 7

what do i solve for though ?

Answer 8

thats the equation ^

Answer 9

you need to solve the curve \(y\)

Answer 10

so implicit differentiation ?

Answer 11

An usual algebraic equation involves isolating a "variable", but a differential equation involves solving for a "curve"

Answer 12

familiar with variable separation ?

Answer 13

yep, give me a sec

Answer 14

https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/separable-equations/v/separable-differential-equations

Answer 15

okay im getting \[\sqrt{C - x^2}\]

Answer 16

is that right?

Answer 17

looks partially correct, show me ur work