Find the equations of all lines that are tangent to the circle x^2+y^2=2y and pass threw the point (0,4). Hint : the line y=mx+4 is tangent to the circle if it intersects the circle at 1 point.
I cant solve this problem. I put my work below but trying to understand my mistakes really might be a waist of time for whoevers reading this. A summery of all my work below is I cant figure out how to make x^2+y^2=2y into a circle. (also the tangent part of the equation looks hard to.)
I dont see how x^2 +y^2=2y is a circle. Is (0,0) the origin? I tried mapping it but if center is origin then y cant be negative. I got :
(x-0)^2 + (y-0)^2 = 2y
But y cant be negative because the left side of equation cant be negative.
Also I realize that square root of 2y cant be radius.
BUT x^2 + (y-1)^2=1 gives me
x cant go anymore positive because y cant be negative in this equation.