Find an equation of a line tangent to a circle x^2+y^2=36 at (6,0).

Question

anonymous · Answer

first you need the slope  
take the derivative wrt x and get 
$$2x+2yy'=0$$
$$2yy'=-2x$$
$$y'=-\frac{x}{y}$$ and now we have problem, because as you can see the slope is undefined at (6,0)
that actually makes the problem easier, because it is therefore a vertical line (we could have seen this if we had graphed the circle with center (00) and radius 6) and the equation for the vertical line is 
$$x=6$$

anonymous · Answer

X=6 OR Y=6 ????????

anonymous · Answer

if this is not a calculus class, then graph the circle and see that the tangent line is vertical

anonymous · Answer

equation for a vertical line looks like 
$$x=\text{number}$$

jamesj · Answer

Step 1 I always say is "sketch a diagram".  

If you do that, you'll notice that (6,0) is the "right most" point on the circle and the tangent there must be a straight line parallel to the y-axis.

jamesj · Answer

attachment

anonymous · Answer

what jamesj said.
if i had paid a slight bit more attention instead of just typing, it would have saved me some time and embarrassment

amistre64 · Answer

or at least some time ;)