Question

Given x^2+y^2=4, find the equation of the tangent line at the point (-1,sq.rt.3). Then, at what point is the slope 0? What point is the slope -1?

I have no clue what to do!

Answer 1

Differentiate the equation: 2x+2ydy/dx=0 2ydy/dx=-2x dy/dx=-x/y dy/dx is the gradient m substitute for x and y m=1/sqrt3 equation for tangent line is y-y1=m(x-x1) where x1 and y1 are -1 and sqrt3 substitute it in equation b)when dy/dx=0 x=0 c)when dy/dx equal -1 x=y

Answer 2

and also draw a picture of the circle of radius 2 and center at (0,0) so you get an idea what is going on.