Question

The chord joining the points where x = p and x = q on the curve
$y=a{x}^2+bx+c$ is parallel to the tangent at the point on the curve whose abscissa is

• A. $\frac{p+q}{2}$
• B. $\frac{p-q}{2}$
• C. $\frac{pq}{2}$
• D. $noneofthese$

Answer 1

The correct option is A $\frac{p+q}{2}$

For $x=p,y=a{p}^2+bp+c$
And for $x=q,y=a{q}^2+bq+c$
$Slope=\frac{a{q}^2+bq+c-a{p}^2-bp-c}{q-p}=a(q+p)+b\frac{dy}{dx}=2ax+b=a(q+p)+b$
(according to the question)
$\therefore x=\frac{q+p}{2}$