Find the tangent lines to the given circle as directed. x^2+y^2=34 at (-3,5).

Given the equation of the line
:

x^2 + y^2 = 34

We need to
find the tangent line at the point ( -3,5)

First we will
differentiate with respect to x.

==> 2x + 2yy' =
0

==> 2yy' =
-2x

==> y' =
-2x/2y

==> y' =
-x/y

Now we will substitute with the point (-3,5) to find
the slope.

==> m = y' = -(-3)/5 =
3/5

Then the equation of the line is given by
:

y-y1 = m(x-x1)

==>
y-5 = (3/5) (x+3)

==> y= (3/5)x + 9/5 +
5

==> y= (3/5)x +
34/5

Then the equation of the line
is:

==> 5y - 3x -34 = 0