Question

A point moves around a circle x^2 + y^2 = 117. When the point is at (6, 9), its x coordinate is increasing at the rate of 10 units per second.How fast is its y coordinate changing at that instant?

Answer 1

Use implicit differentiation.

Answer 2

Can you do that?

Answer 3

differentiate with respect to \(t\).

Answer 4

Do you want more help?

Answer 5

yes, because I keep getting wrong answer. I know it's -x/y, but I cant go further

Answer 6

Both \(x\) and \(y\) are functions of \(t\).

Answer 7

So what it would be?

Answer 8

\[
\frac{dx^2}{dt}=\frac{dx^2}{dx}\frac{dx}{dt} = 2x\frac{dx}{dt}
\]

Answer 9

but what about y?

Answer 10

It's completely symmetric for \(y\). So the equation is: \[
2x\frac{dx}{dt}+2y\frac{dy}{dt}=0
\]

Answer 11

but dx/dt is 10, right?

Answer 12

Yes

Answer 13

and you solve for dy/dt?

Answer 14

Yes.

Answer 15

And plug in (6, 9) for x and y.

Answer 16

ohhhhhh,thank you guys sooooo much!