Question

The shortest distance of $\left(0,3\right)$ from the parabola $y=x^2$ is

• A. $\sqrt{3}$ units
• B. $\frac{\sqrt{11}}{2}$ units
• C. $\frac{\sqrt{10}}{2}$ units
• D. $\frac{5}{2}$ units

Answer 1

Answer: (B)

Any point on the parabola is $\left(x,x^2\right)$
Distance between $\left(x,x^2\right)$ and $(0,3)$ is $D=\sqrt{x^2+{\left(x^2-3\right)}^2}$
$D^2={\left(x^2-\frac{5}{2}\right)}^2+3-\frac{1}{4}$ is minimum
if $x^2-\frac{5}{2}=0$
Hence, $D_{\min }=\sqrt{\frac{11}{4}}=\frac{\sqrt{11}}{2}$ units