Question

The shortest distance from $(0,3)$ to the parabola $y^2=4x$ is

• A. $2$
• B. $\sqrt{2}$
• C. $5$
• D. $\sqrt{5}$

Answer 1

The correct option is B $\sqrt{2}$

The shortest distance from $(0,3)$ to parabola $y^2=4x$ is:

S=distance=$\sqrt{(x-0{)}^2+(y-3{)}^2}$

$S^2=x^2+{(y-3)}^2{y}^2=4xP=S^2=\frac{y^4}{16}+{(y-3)}^2\frac{dP}{dt}=\frac{y^3}{4}+2(y-3)=0y^3+8y-24=0y=2x=1S=\sqrt{1^2+(2-3{)}^2}=\sqrt{2}$