Question 294471
it works, in this case, because the circle is centered at the origin


since the center is at the origin, the slope of a radius to any point (x,y) on the circle is y/x


a tangent is perpendicular to the radius at the point of tangency, so the slope of the tangent is -x/y


substituting, the equation for the tangent is ___ y = (-x/y)x + k


multiplying by y ___ y^2 = (-x)x + (ky) ___ y^2 = -x^2 + (ky)


adding x^2 ___ y^2 + x^2 = ky


dividing by y ___ (y^2 + x^2) / y = k ___ r^2 / y = k