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Two tangents

Source: Reddit
Find a line which is tangent to the curve $$y=x^4-4x^3$$ at 2 points.

Bézier curve

A Bézier curve is created as follows:
1) A set of points $$P_0$$, ..., $$P_n$$ are chosen (in the example $$n=4$$).
2) A set of points $$Q_0$$, ..., $$Q_{n-1}$$ are defined by $$Q_i=t P_{i+1}+(1-t) P_i$$ (shown in green).
3) A set of points $$R_0$$, ..., $$R_{n-2}$$ are defined by $$R_i=t Q_{i+1}+(1-t) Q_i$$ (shown in blue).
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$$n$$) After repeating the process $$n$$ times, there will be one point. The Bézier curve is the path traced by this point at $$t$$ varies between 0 and 1.

What is the Cartesian equation of the curve formed when:
$$P_0=\left(0,1\right)$$ $$P_1=\left(0,0\right)$$ $$P_2=\left(1,0\right)$$

Two lines

Let A and B be two straight lines such that the gradient of A is the y-intercept of B and the y-intercept of A is the gradient of B (the gradient and y-intercept of A are not the same). What are the co-ordinates of the point where the lines meet?