Let
be a point on the curve. Then this point satisfies
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
.