Angle between the lines 2 x^2-3 x y+y^2=0 is - Vidyadip

MCQ

Angle between the lines $2 x^2-3 x y+y^2=0$ is

A
$\tan ^{-1}(\sqrt{3})$
B
$\cot ^{-1}(\sqrt{3})$
✓
$\cot ^{-1}(3)$
D
$\tan ^{-1}\left(\frac{1}{\sqrt{3}}\right)$

✓

Answer

Correct option: C.

$\cot ^{-1}(3)$

(C) Given equation of pair of lines is
$2 x^2-3 x y+y^2=0$
$\therefore \quad a=2, h=\frac{-3}{2}, b=1$
$\therefore \quad \tan \theta=\left|\frac{2 \sqrt{\frac{9}{4}-2}}{3}\right|=\left|\frac{\sqrt{9-8}}{3}\right|=\frac{1}{3}$
$\therefore \cot \theta=3 \Rightarrow \theta=\cot ^{-1}$ (3)

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from Pair of Straight Lines→Pair of Straight Lines — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Let $\text{f}:\text{R}-\Big\{\frac{3}{5}\Big\}\rightarrow\ \text{R}$ be defined by $\text{f(x)}=\frac{3\text{x}+2}{5\text{x}-3}.$ Then,

If the function $f(x) = x^2 - kx + 5$ is increasing on $[2, 4]$, then:

$\int_{-\pi / 2}^{\pi / 2} \log \left(\frac{2-\sin x}{2+\sin x}\right) d x=$

$Q^+$ denote the set of all positive rational numbers. If the binary operation $\text{a }\odot$ on $Q^+$ is defined as:
$\text{a }\odot=\frac{\text{ab}}{2}$, then the inverse of $3$ is:

If p ∧ q is F, p → q is F then the truth values of p and q are ________.

If $\sin \theta+\cos \theta=1$, then the general value of $\theta$ is

The angle between two planes $x+2 y+2 z=3$ and $-5 x+3 y+4 z=9$ is

$\bar{a}$ and $\bar{b}$ are unit vectors. If $\bar{a}+\bar{b}$ is a unit vector, then the angle between $\overline{ a }$ and $\overline{ b }$ is

Differential coefficient of $\sec(\tan^{-1}\text{x})$ is:

If the mean and variance of a binomial distribution are 18 and 12 respectively, then n = ___________