Question

The shortest distance between the line $y-x=1$ and the curve $x = y^2$ is

• A. $\frac{3\sqrt{2}}{8}$
• B. $\frac{2\sqrt{3}}{8}$
• C. $\frac{3\sqrt{2}}{5}$
• D. $\frac{\sqrt{3}}{4}$

Answer 1

Answer: (A)

$\frac{3\sqrt{2}}{8}$

Answer 2

$x - y + 1= 0 \dots\left(1\right)$ $x=y^{2}$ $1-2y \frac{dy}{dx} \Rightarrow \frac{dy}{dx}=\frac{1}{2y}=$ Slope of given line $\left(1\right)$ $\frac{1}{2y}=1 \Rightarrow y=\frac{1}{2} \Rightarrow x=\left(\frac{1}{2}\right)^{2}=\frac{1}{4} \Rightarrow \left(x, y\right)=\cdot\left(\frac{1}{4}, \frac{1}{2}\right)$ $\therefore$ The shortest distance is $\frac{\left|\frac{1}{4}-\frac{1}{2}+1\right|}{\sqrt{1+1}}=\frac{3}{4\sqrt{2}}=\frac{3\sqrt{2}}{8}$ Question number 86 to 90 are Assertion - Reason type questions. Each of these questions contains two statements Each of these questions also have four alternative choices, only one of which is the correct answer. You have to select the correct choice