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

If $\frac{1-\tan ^2 \theta}{\sec ^2 \theta}=\frac{1}{2}$, then the general value of $\theta$ is

$\sin ^{-1} \frac{1}{\sqrt{5}}+\cot ^{-1} 3$ is equal to

The distance of the point (3, 4, 5) from Y- axis is

The plane containing the lines $\frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7}$ and $\frac{x-2}{1}=\frac{y-4}{4}=\frac{z-6}{7}$ passes through

If $X$ is a random variable with probability distribution as given below:

$X = x_i$	$0$	$1$	$2$	$3$
$P(X = X_i)$	$k$	$3k$	$3k$	$k$

The value of $k$ and its variance are:

Direction cosines of the line $\frac{x+2}{2}=\frac{2 y-5}{3}, z=-1$ are

The probability distribution of X is

X	0	1	2	3
P(X)	0.3	k	2k	2k

The value of k is

If $\text{A}=\begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{bmatrix},$ then $A^5 =$

The function $\text{f}(\text{x})=\log_\text{e}\Big(\text{x}^3+\sqrt{\text{x}^6+1}\Big)$ is of the following type:

For any two vectors $\bar{a}$ and $\bar{b}$ which of the following is true?