Let be a point on the curve. Then
To find the slope of the tangent line passing through , use implicit differentiation. Differentiate both sides of the equation of the curve with respect to . By the chain rule,
Let be the slope of the tangent line at point . Assume . Then
Using the point-slope formula, the tangent line equation to the curve at the point can be written as
Let this tangent line pass through . Putting and ,
Together with Equation (1) we can solve for the point. or
Now consider if , then The slope of the tangent line DNE. It follows that the tangent line is a vertical line, either or . Neither of them passes through the point
Therefore, the points on the curve that satisfy the requirements are .