Question

Suppose a curve C such that its slope is dy/dx= -x/y. If C passes through the point (-4, 3), answer the following.
a) Find an equation for the curve.
b) Find the points where the curve has a vertical tangent line.

Answer 1

okay! i solved part a. the equations is sqrt(25-x) = y(x)
how do i do part b?

Answer 2

you should get \(y(x) = \pm \sqrt{25-x^2}\)

Answer 3

its a circle of radius 5

Answer 4

use below for part b :
vertical tangents occur when slope is undefined

Answer 5

would it be 25?

Answer 6

what would be 25 ?

Answer 7

x=25 is where a tangent line is?

Answer 8

nope

Answer 9

\(\large \frac{dy}{dx} = \frac{-x}{y}\)

slope has "undefined" value when the denominator, \(y = 0\)

Answer 10

so the x values where the tangent is vertical can be found by setting y = 0 :

\(\sqrt{25-x^2} = 0\)

solve \(x\)

Answer 11

oh! okay thanks!

Answer 12

np :)