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