Let (α, β) be an ordered pair of real numbers satisfying the equation x2-4 x+4 y2+3=0. If the maximum and minimum values of √α2+β2 are l and s respectively, then the value of (l-s/l+s) is equal to

Question

Let (α, β) be an ordered pair of real numbers satisfying the equation x2-4 x+4 y2+3=0. If the maximum and minimum values of √α2+β2 are l and s respectively, then the value of (l-s/l+s) is equal to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/e64e68755ff94f316bf85fb3e38e474d-.png" /> √α2+β2 represents the distance of α, 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 ⇒ (l- s /l+ s )=(2/4)=0.5

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

$α^{2} + β^{2}$ represents the distance of $α, β$ 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 $s = O A = 1$
$\Rightarrow \frac{l - s}{l + s} = \frac{2}{4} = 0.5$

Q. Let (α,β) be an ordered pair of real numbers satisfying the equation x2−4x+4y2+3=0. If the maximum and minimum values of α2+β2​ are l and s respectively, then the value of l+sl−s​ is equal to

α2+β2​ represents the distance of α,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 ⇒l+sl−s​=42​=0.5

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

$α^{2} + β^{2}$ represents the distance of $α, β$ 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 $s = O A = 1$
$\Rightarrow \frac{l - s}{l + s} = \frac{2}{4} = 0.5$