Find the derivative to the equation of the circle ( x^2 + y^2 - 2x + 4y - 4 = 0 )

Question

asked Sep 15, 2020 26.3k views

1 Answer

Maximilian Stroh · Answer 1 · 2020-09-21T15:41:54+0000

Answer:

(dy)/(dx) =(1-x)/(y+2)

Explanation:

We begin with the equation
x^2+y^2-2x+4y-4=0

Next, we need to differentiate with respect to x

2x+2y(dy)/(dx) -2+4(dy)/(dx) =0

Now we need to solve for
(dy)/(dx)

To do this, we need to factor out the
(dy)/(dx) and then isolate it.

$2x+2y(dy)/(dx) -2+4(dy)/(dx) =0\\\\2y(dy)/(dx)+4(dy)/(dx)=2-2x\\\\(dy)/(dx)(2y+4)=2-2x\\\\(dy)/(dx)=(2-2x)/(2y+4)\\\\(dy)/(dx)=(1-x)/(y+2)$