Question

The straight line $y=mx+c(m>0)$ touches the parabola $y^2=8(x+2)$ then the minimum value taken by $c$ is

• A. $4$
• B. $8$
• C. $12$
• D. $6$

Answer 1

The correct option is A $4$

The tangent of slope m must be of the form

$y=m(x+2)+\frac{a}{m}$

$2m+\frac{2}{m}=c$

$c=2(m+\frac{1}{m})\ge 2\times 2$

$\therefore C_{min}\ge 4$

$\therefore C_{min}=4$.