enEnglishguગુજરાતી
JEE Mains · Maths · STD 12 - 6. Application of derivatives
The shortest distance between the line \(x-y=1\) and the curve \(x^{2}=2 y\) is .... .
- A \(\frac{1}{2}\)
- B \(\frac{1}{2 \sqrt{2}}\)
- C \(\frac{1}{\sqrt{2}}\)
- D \(0\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{2 \sqrt{2}}\)
Step-by-step Solution
Detailed explanation
Shortest distance between curves is always along common normal. \(\left.\frac{ dy }{ dx }\right|_{ P }=\) slope of line \(=1\) \(\Rightarrow x_{0}=1 \quad \therefore y_{0}=\frac{1}{2}\) \(\Rightarrow P \left(1, \frac{1}{2}\right)\) \(\therefore\) Shortest distance…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The curve satisfying the differential equation, \(ydx-(x + 3y^2 )\, dy = 0\) and passing through the point \((1, 1)\) , also passes through the pointJEE Mains 2017 Hard
- Let the vectors \(\vec{a}, \vec{b}, \vec{c}\) represent three coterminous edges of a parallelopiped of volume V. Then the volume of the parallelopiped, whose coterminous edges are represented by \(\vec{a}, \vec{b}+\vec{c}\) and \(\vec{a}+2 \vec{b}+3 \vec{c}\) is equal to \(..........\,V\)JEE Mains 2023 Medium
- The area (in sq. units) of the region described by \(\left\{(\mathrm{x}, \mathrm{y}): \mathrm{y}^2 \leq 2 \mathrm{x}\right.\), and \(\left.\mathrm{y} \geq 4 \mathrm{x}-1\right\}\) isJEE Mains 2024 Medium
- If three positive numbers \(a, b\) and \(c\) are in \(A.P.\) such that \(abc\, = 8\), then the minimum possible value of \(b\) isJEE Mains 2017 Hard
- The integral \(\int{ \cfrac{d x}{(x+4)^{\frac{8}{7}}(x-3)^{\frac{6}{7}}}}\) is equal to (where \(\mathrm{C}\) is a constant of integration)JEE Mains 2020 Hard
- Let \(\mathrm{f}: N \rightarrow N\) be a function such that \(\mathrm{f}(\mathrm{m}+\mathrm{n})=\mathrm{f}(\mathrm{m})+\mathrm{f}(\mathrm{n})\) for every \(\mathrm{m}, \mathrm{n} \in N\). If \(\mathrm{f}(6)=18\) then \(\mathrm{f}(2) \cdot \mathrm{f}(3)\) is equal to :JEE Mains 2021 Hard
More PYQs from JEE Mains
- The remainder when \(19^{200}+23^{200}\) is divided by \(49\) , is \(.........\).JEE Mains 2023 Hard
- In a game two players \(A\) and \(B\) take turns in throwing a pair of fair dice starting with player \(A\) and total of scores on the two dice, in each throw is noted. \(A\) wins the game if he throws a total of \(6\) before \(B\) throws a total of \(7\) and \(B\) wins the game if he throws a total of \(7\) before \(A\) throws a total of six The game stops as soon as either of the players wins. The probability of \(A\) winning the game isJEE Mains 2020 Hard
- Let \(e_{1}\) and \(e_{2}\) be the eccentricities of the ellipse, \(\frac{x^{2}}{25}+\frac{y^{2}}{b^{2}}=1(b<5)\) and the hyperbola \(\frac{ x ^{2}}{16}-\frac{ y ^{2}}{ b ^{2}}=1\) respectively satisfying \(e _{1} e _{2}=1 .\) If \(\alpha\) and \(\beta\) are the distances between the foci of the ellipse and the foci of the hyperbola respectively, then the ordered pair \((\alpha, \beta)\) is equal toJEE Mains 2020 Hard
- The line, that is coplanar to the line \(\frac{x+3}{-3}=\frac{y-1}{1}=\frac{z-5}{5}\), isJEE Mains 2023 Medium
- Let a curve \(y=f(x)\) pass through the point \(\left(2,\left(\log _{e} 2\right)^{2}\right)\) and have slope \(\frac{2 y}{x \log _{e} x}\) for all positive real value of \(x\). Then the value of \(f(e)\) is equal to \(.....\)JEE Mains 2021 Easy
- If the function \( f(x) = \frac{e^{x}(e^{\tan x-x}-1)+\log_{e}(\sec x+\tan x)-x}{\tan x-x} \) is continuous at \( x=0 \), then the value of \( f(0) \) is equal toJEE Mains 2026 Hard