Question 194785
i have to write an equation of the line that is tangent to the circle at that point:

x^2+y^2=50; (-7,1)
<pre><font size = 4 color = "indigo"><b>
Find the derivative by the method of implicit functions

{{{x^2+y^2=50}}}

{{{2x+2y(dy/dx)=0}}}

{{{2y(dy/dx)=-2x}}}

{{{dy/dx=(-2x)/(2y)}}}

{{{dy/dx=-x/y}}}

Substitute (x,y)=(-7,1)

{{{dy/dx=-(-7)/1}}}

{{{dy/dx=7}}}

Therefore the slope, m, of the tangent line
at (-7,1) is 7.  So m=7

Now we use the point-slope form of the
equation of a line:

{{{y-y[1]=m(x-x[1])}}}

{{{y-1=7(x-(-7))}}}

{{{y-1=7(x+7)}}}

{{{y-1=7x+49}}}

{{{y = 7x+50}}}

To check it we draw the equation of the circle
and the line:

{{{drawing(400,400,-10,10,-10,10,line(-7.15,1,-6.85,1),
locate(-6.8,1.4,"(-7,1)"),
graph(400,400,-10,10,-10,10,7x+50), circle(0,0,sqrt(50)) )}}}

Edwin</pre>