Question

Use implicit differentiation to find the negative slope of a tangent to the circle x^2+y^2=16 at x=-2

Answer 1

slope = -
`(√(3) )/(3)`

Explanation:

Differentiating implicitly with respect to x

2x + 2y
`(dy)/(dx)` = 0

2y
`(dy)/(dx)` = - 2x

`(dy)/(dx)` = -
`(2x)/(2y)` = -
`(x)/(y)`

`(dy)/(dx)` is the measure of the slope of the tangent

rearrange equation to find corresponding y-coordinate of x = - 2

y² = 16 - 4 = 12 = 2
`√(3)` ⇒ y = ± 2
`√(3)`

using x = - 2, y = - 2
`√(3)`, then

`(dy)/(dx)` = -
`(1)/(√(3) )` = -
`(√(3) )/(3)`