Hello, kamkal!

You're mixing your x's . . .

1) Find the equations of all tangents to the graph of: .

that passes through the origin (0,0).

Let the point be on the parabola.

. . Note that: . .[1]

A tangent to the curve has slope: .

At point , the slope is: .

The equation of the line through with slope is:

. .

Substitute [1]: .

. . which simplifies to: . .[2]

Since is on this tangent, we have:

. .

Substitute into [2]: