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. $p+q$

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 $=\frac{a{q}^2+bq+c-a{p}^2+bq+c}{q-p}$
For =a(q+q)+b
$\frac{dy}{dx}=2ax+b=a(q+p)+b\therefore x=\frac{q+p}{2}$