The distance between the two points A and A prime which lie on y =2 such that both the line segments AB and A prime B (where B is the point (2,3) ) subtend angle (π/4) at the origin, is equal to :

Question

The distance between the two points A and A prime which lie on y =2 such that both the line segments AB and A prime B (where B is the point (2,3) ) subtend angle (π/4) at the origin, is equal to : (A) 10 (B) (48/5) (C) (52/5) (D) 3

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/21cc0b75c6812006b0f158c9af6ae430-.png" /> M1=3 / 2 M2=2 / x tan π / 4=|(3 / 2-2 / x/1+6 / 2 x)|=1 ⇒ x1=10, x2=-2 / 5 ⇒ AA 1=52 / 5

Q. The distance between the two points $A$ and $A^{'}$ which lie on $y = 2$ such that both the line segments $A B$ and $A^{'} B$ (where $B$ is the point $(2, 3)$ ) subtend angle $\frac{π}{4}$ at the origin, is equal to :

$10$

$\frac{48}{5}$

$\frac{52}{5}$

$3$

$M_{1} = 3/2 M_{2} = 2/ x$
$tan π /4 = ∣ ∣ \frac{3/2 - 2/ x}{1 + 6/2 x} ∣ ∣ = 1$
$\Rightarrow x_{1} = 10, x_{2} = - 2/5$
$\Rightarrow A A^{1} = 52/5$

Q. The distance between the two points A and A′ which lie on y=2 such that both the line segments AB and A′B (where B is the point (2,3) ) subtend angle 4π​ at the origin, is equal to :

10

548​

552​

3

M1​=3/2M2​=2/x tanπ/4=∣∣​1+6/2x3/2−2/x​∣∣​=1 ⇒x1​=10,x2​=−2/5 ⇒AA1=52/5

Q. The distance between the two points $A$ and $A^{'}$ which lie on $y = 2$ such that both the line segments $A B$ and $A^{'} B$ (where $B$ is the point $(2, 3)$ ) subtend angle $\frac{π}{4}$ at the origin, is equal to :

$10$

$\frac{48}{5}$

$\frac{52}{5}$

$3$

$M_{1} = 3/2 M_{2} = 2/ x$
$tan π /4 = ∣ ∣ \frac{3/2 - 2/ x}{1 + 6/2 x} ∣ ∣ = 1$
$\Rightarrow x_{1} = 10, x_{2} = - 2/5$
$\Rightarrow A A^{1} = 52/5$