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

Question

Dr. Abubacker · Accepted Answer

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

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

Explanation

Reviewed by Dr. Abubacker

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