#28 Measure you Calibre

Solution:

As the lines are parallel , their slopes must be equal.

Slope of chord:

$\begin{aligned}\frac{y_2-y_1}{x_2-x_1}&=\frac{227-5}{11-5}\\&=\frac{222}{6}\\ &=37\hspace{2cm} \cdots(1)\end{aligned}$

Slope of curve= Derivative of the equation of the curve.

$\begin{aligned}\large y&=3x^{2}-11x-15\\ \frac{dy}{dx}&=6x-11\hspace{2cm}\cdots(2)\end{aligned}$

Equating $(1)$ and $(2)$ we get,

$\begin{aligned}6x-11=37\\ x=8\end{aligned}$

$\therefore$ Abscissa or $x$ -coordinate of the point is $\boxed{8}$