Let (a , β ) be an ordered pair of real numbers satisfying the equation x2-4x+y2+3=0. If the maximum and minimum values of √a2 + β 2 are l and s respectively, then the value of 2((l - s/l + s)) is equal to

Question

Let (a , β ) be an ordered pair of real numbers satisfying the equation x2-4x+y2+3=0. If the maximum and minimum values of √a2 + β 2 are l and s respectively, then the value of 2((l - s/l + s)) is equal to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-bbuuaradljsyythy.jpg" /> √a2 + β 2 represents the distance of (a , β ) from the origin (0,0) . Now, let the line joining O(0 , 0) and center of circle C(2,0) cuts the circle at points (1,0)=A and (3,0)=B ,then, l=OB=3 and s=OA=1 ⇒ 2((l - s/l + s))=1

Q. Let $(a, β)$ be an ordered pair of real numbers satisfying the equation $x^{2} - 4 x + y^{2} + 3 = 0.$ If the maximum and minimum values of $a^{2} + β^{2}$ are $l$ and $s$ respectively, then the value of $2 (\frac{l - s}{l + s})$ is equal to

$a^{2} + β^{2}$ represents the distance of $(a, β)$ from the origin $(0, 0)$ .
Now, let the line joining $O (0, 0)$ and center of circle $C (2, 0)$ cuts the circle at points $(1, 0) = A$ and $(3, 0) = B$ ,then, $l = OB = 3$ and $s = O A = 1$
$\Rightarrow 2 (\frac{l - s}{l + s}) = 1$

Q. Let (a,β) be an ordered pair of real numbers satisfying the equation x2−4x+y2+3=0. If the maximum and minimum values of a2+β2​ are l and s respectively, then the value of 2(l+sl−s​) is equal to

a2+β2​ represents the distance of (a,β) from the origin (0,0) . Now, let the line joining O(0,0) and center of circle C(2,0) cuts the circle at points (1,0)=A and (3,0)=B ,then, l=OB=3 and s=OA=1 ⇒2(l+sl−s​)=1

Q. Let $(a, β)$ be an ordered pair of real numbers satisfying the equation $x^{2} - 4 x + y^{2} + 3 = 0.$ If the maximum and minimum values of $a^{2} + β^{2}$ are $l$ and $s$ respectively, then the value of $2 (\frac{l - s}{l + s})$ is equal to

$a^{2} + β^{2}$ represents the distance of $(a, β)$ from the origin $(0, 0)$ .
Now, let the line joining $O (0, 0)$ and center of circle $C (2, 0)$ cuts the circle at points $(1, 0) = A$ and $(3, 0) = B$ ,then, $l = OB = 3$ and $s = O A = 1$
$\Rightarrow 2 (\frac{l - s}{l + s}) = 1$