Question

The chord joining the points $(5,5)$ and $(11,227)$ on the curve $y=3x^2-11x-15$ is parallel to tangent at a point on the curve. Then, the abscissa of the point is

• A. $-4$
• B. $4$
• C. $-8$
• D. $8$
• E. $6$

Answer 1

Answer: (D)

$8$

Let the required point be $P(x_1,y_1)$. The equation of the given curve is
$y=3x^2-11x-15$
$\Rightarrow \frac{dy}{dx}=6x-11$
$\Rightarrow {\left(\frac{dy}{dx}\right)}_{(x_1,y_1)}=6x_1-11$
Since, the tangent at $P$ is parallel to the line joining $(5,5)$ and $(11,227)$.
Therefore, slope of the tangent at $P=$ Slope of the line joining $(5,5)$ and $(11,227)$.
$\Rightarrow {\left(\frac{dy}{dx}\right)}_{(x_1,y_1)}=\frac{227-5}{11-5}$
$\Rightarrow 6x_1-11=\frac{222}{6}$
$\Rightarrow 6x_1-11=37$
$\Rightarrow 6x_1=48\Rightarrow x_1=8$