Question

The equation of the tangent to the parabola $y=(x-3)^2$ parallel to the chord joining the points $(3,0)$ and $(4,1)$ is:

• A. $2 x-2 y+6=0$
• B. $2 y-2 x+6=0$
• C. $4 y-4 x+11=0$
• D. $4 x-4 y=13$

Answer 1

Answer: (D)

Slope of tangent $=\frac{1-0}{4-3}=1$
also $ \frac{d y}{d x}=2(x-3)$
$\left(\frac{d y}{d x}\right)_{\left(x_1, y_1\right)}=2(x,-3)=1 \Rightarrow x_1-3=\frac{1}{2} $
$x_1=\frac{7}{2} $
$\therefore y_1=\left(\frac{7}{2}-3\right)^2=\frac{1}{4}$
Equation of tangent is
$y-\frac{1}{4}=1\left(x-\frac{7}{2}\right)$
$4 y-1=2(2 x-7) $
$4 x-4 y=13$