Category:Area of Triangle Inscribed in Parabola

This category contains pages concerning Area of Triangle Inscribed in Parabola:

Let $T$ be the parabola which is the locus of points $\tuple {x, y}$ satisfying $y = x^2$.

Let $A$ and $B$ be two arbitrary points on $T$ with coordinates:

$A = \tuple {u, u^2}$

$B = \tuple {v, v^2}$, with $u > v$

Let $C$ be a third point on $T$ whose $x$-coordinate is the average of those of $A$ and $B$.

The area of $\triangle ABC$ is:

$\map \AA {\triangle ABC} = \dfrac 1 8 \paren {u - v}^3$