Download App

STD 11 - 9. straight line — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 9. straight line4 Marks
MCQ
Angle between the lines $\frac{x}{a} + \frac{y}{b} = 1$ and $\frac{x}{a} - \frac{y}{b} = 1$ is
  • ✓
    $2{\tan ^{ - 1}}\frac{b}{a}$
  • B
    ${\tan ^{ - 1}}\frac{{2ab}}{{{a^2} + {b^2}}}$
  • C
    ${\tan ^{ - 1}}\frac{{{a^2} - {b^2}}}{{{a^2} + {b^2}}}$
  • D
    None of these
✓

Answer

Correct option: A.
$2{\tan ^{ - 1}}\frac{b}{a}$
a
(a)The lines are $bx + ay - ab = 0$ and $bx - ay - ab = 0$.

Hence the required angle is

${\tan ^{ - 1}}\left| {\frac{{ab - ( - ab)}}{{{b^2} + ( - {a^2})}}} \right| = {\tan ^{ - 1}}\left| {\frac{{2ab}}{{{b^2} - {a^2}}}} \right| = 2{\tan ^{ - 1}}\frac{b}{a}$.

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Suppose $f ( x )$ is a polynomial of degree four, having critical points at $-1,0,1$ . If $T =\{ x \in R \mid f ( x )= f (0)\},$ then the sum of squares of all the elements of $T$ is
→
Let $N$ denotes the sum of the numbers obtained when two dice are rolled. If the probability that $2^{ N } < N !$ is $\frac{m}{n}$, where $m$ and $n$ are coprime, then $4 m -3 n$ is equal to $......$.
→
The equation of the tangent to the circle ${x^2} + {y^2} = {r^2}$ at $(a,b)$ is $ax + by - \lambda = 0$, where $\lambda $ is
→
The number of elements in the set $S =\left\{\theta \in[0,2 \pi]: 3 \cos ^4 \theta-5 \cos ^2 \theta-2 \sin ^2 \theta+2=0\right\}$ is $...........$.
→
If $y = 2sin^{-1} \sqrt {(1-x)} + sin^{-1} (2\sqrt{x(1-x)})$ for $0 < x < \frac{1}{2}$, then $\frac{dy}{dx}$ equals-
→
If $\cos A = \frac{3}{4}$, then $32\sin \frac{A}{2}\cos \frac{5}{2}A = $
→
Let $ABCD$ be a square of side of unit length. Let a circle $C _{1}$ centered at $A$ with unit radius is drawn. Another circle $C _{2}$ which touches $C _{1}$ and the lines $AD$ and $AB$ are tangent to it, is also drawn. Let a tangent line from the point $C$ to the circle $C _{2}$ meet the side $AB$ at $E$. If the length of $EB$ is $\alpha+\sqrt{3} \beta,$ where $\alpha, \beta$ are integers, then $\alpha+\beta$ is equal to.........
→
Set $A$ has $3$ elements and set $B$ has $4$ elements. The number of injection that can be defined from $A$ to $B$ is
→
Let $a_{1}, a_{2} \ldots, a_{n}$ be a given $A.P.$ whose common difference is an integer and $S _{ n }= a _{1}+ a _{2}+\ldots+ a _{ n }$ If $a_{1}=1, a_{n}=300$ and $15 \leq n \leq 50,$ then the ordered pair $\left( S _{ n -4}, a _{ n -4}\right)$ is equal to
→
If the circle ${x^2} + {y^2} = {a^2}$ cuts off a chord of length $2b$ from the line $y = mx + c$, then
→