A tangent is drawn to the circle 2x2 + 2y2 - 3x + 4y = 0 at the point A and it meets the line x + y = 3 at B(2, 1), then AB is equal to

Question

A tangent is drawn to the circle 2x2 + 2y2 - 3x + 4y = 0 at the point A and it meets the line x + y = 3 at B(2, 1), then AB is equal to (A) √ 10 (B) 2 (C) 2√ 2 (D) 0

Tardigrade Admin · Accepted Answer

Equation of circle is, S ≡ 2 x2+2 y2-3 x+4 y=0 ⇒ S ≡ x2+y2-(3/2) x+2 y=0 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/949d708e9f86723f3ff9311f249a50ad-.png" /> Here, A B is the length of tangent to the circle from B i.e. A B =√(2)2+(1)2-(3/2)(2)+2(1) =√4+1-3+2=√4 =2 units

Q. A tangent is drawn to the circle $2 x^{2} + 2 y^{2} - 3 x + 4 y = 0$ at the point A and it meets the line $x + y = 3$ at $B (2, 1)$ , then AB is equal to

$10$

$2$

$22$

$0$

Equation of circle is,
$S \equiv 2 x^{2} + 2 y^{2} - 3 x + 4 y = 0$
$\Rightarrow S \equiv x^{2} + y^{2} - \frac{3}{2} x + 2 y = 0$

Here, $A B$ is the length of tangent to the circle from $B$
i.e. $A B = (2)^{2} + (1)^{2} - \frac{3}{2} (2) + 2 (1)$
$= 4 + 1 - 3 + 2 = 4$
$= 2$ units

Q. A tangent is drawn to the circle 2x2+2y2−3x+4y=0 at the point A and it meets the line x+y=3 at B(2,1), then AB is equal to

10​

2

22​

0

Equation of circle is, S≡2x2+2y2−3x+4y=0 ⇒S≡x2+y2−23​x+2y=0 Here, AB is the length of tangent to the circle from B i.e. AB=(2)2+(1)2−23​​(2)+2(1) =4+1−3+2​=4​ =2 units

Q. A tangent is drawn to the circle $2 x^{2} + 2 y^{2} - 3 x + 4 y = 0$ at the point A and it meets the line $x + y = 3$ at $B (2, 1)$ , then AB is equal to

$10$

$2$

$22$

$0$

Equation of circle is,
$S \equiv 2 x^{2} + 2 y^{2} - 3 x + 4 y = 0$
$\Rightarrow S \equiv x^{2} + y^{2} - \frac{3}{2} x + 2 y = 0$

Here, $A B$ is the length of tangent to the circle from $B$
i.e. $A B = (2)^{2} + (1)^{2} - \frac{3}{2} (2) + 2 (1)$
$= 4 + 1 - 3 + 2 = 4$
$= 2$ units