what is the equation for a line tangent to x2+y2=25 at point (3,4)? and how do you get that answer?

Question

what is the equation for a line tangent to x2+y2=25 at point (3,4)?  and how do you get that answer?

anonymous · Answer

Take a derivative. Plug in (3,4) that gives you the slope. Then use point slope form:
$$y-y_0=m(x-x_0)$$
To get the equation of the line.

amistre64 · Answer

y = f'(3) -3f'(3) +4

amistre64 · Answer

the derivative is determined by the same rules that apply to any derivative; x^2 goes to 2x.x' ;  y^2 goes to 2y.y'  and 25 goes to 0

2x.x' + 2y.y' = 0 ; solve for y'

anonymous · Answer

I'm probably the worst at math. 
what's a derivative?

amistre64 · Answer

a derivative is:

$$\lim_{h->0}\frac{f(x+h)-f(x)}{h}$$

but that is just how we learn to get the derivative; after that we learn that there are simple rules that derivatves follow

amistre64 · Answer

the derivative of a function allows us to see the slope of the tangent line at any given point of that function

amistre64 · Answer

in any event, I did the hard stuff for you; now all you have to do is algebra this equation to solve for y':

2x.x' + 2y.y' = 0 ; solve for y'

anonymous · Answer

okay thank you so much! this will really help with my placement test coming up! i hate math!