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.
  
• B.
  
• C.
  
• D. None of these

Answer 1

The correct option is A

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
$\frac{dy}{dx}=2ax+b=a(q+p)+b\therefore x=\frac{q+p}{2}$