Proportionality of triangles problem

[darkmagic]

Homework Statement

Is any formulas similar to that of proportionality of the triangles to proportionality of the given figure?

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

Not in general, no. How is that curve defined?

 

[darkmagic]

the curve is a parabola

 

[CompuChip]

What do you mean by "proportionality"?
That if you magnify area I by some appropriate factor, that you can perfectly fit it over area II? Because that is not true.

Or do you mean: some formula for y₂ / y₁ given x₂ / x₁ (where y_i is the function value on the right of area i with x-value x_i)?

 

[darkmagic]

proportionality x1/x2=y1/y2

 

[CompuChip]

$$\frac{x_1}{x_2} = \frac{a x_1^2 + b x_2 + c}{a x_2^2 + b x_2 + c}$$

where $ax^2 + bx + c$ is the formula for the parabola?