Finding the equations for the lines that are tangent and normal to the given point.?

I was given a derivative formula in which I had to use to find the slope and I ended up having a slope of 1/-2 and the given point is (1,1)

I was asked to find the tangent line which is the x and normal like which is the y.

I really don’t know what its asking so it would be appreciated to have some help with it.

My professor said something about the tan line’s fomula being (x-b)=m(x-a)

And the normal line formula being (y-b)=-1/m (x-a)

But I didn’t quite get it.

Also just another quick question to confirm my answer.

I was asked to give the equation of the line with two points, one having the center which was (2,-3) and radius of 3 and the other was (-3,-2) with radius of 2.

Was I suppose to use y-y1 = (y2-y1/x2-x1)(x-x1)

Because I did that and I got (y+3) = -1/5(x-2)

Thanks for the all the help