Question

Find a point on the parabola $y=(x-4{)}^2$, where the tangent is parallel to the chord joining $(4,0)$ and $(5,1)$.

Answer 1

As tangent is parallel to the chord passing through given points, Therefore their slopes will be equal.

Slope of chord,

$m=\frac{1-0}{5-4}=1$

Differentiating the given equation, we get

$\frac{dy}{dx}=2(x-4)=1$

$⟹x=\frac{9}{2}$

On putting value of $x$ in given parabolic equation, we get

$y=+\frac{1}{4}$ and $y=-\frac{1}{4}$