if ( a , b ) ∈ A ∩ B ∩ C , then ( a + 1 ) 2 + ( a − 5 ) 2 + 2 ( b − 1 ) 2 lies in which interval?

The expression equals 2 [ ( a − 2 ) 2 + b 2 ] + 20 − 4 b = 38 − 4 b . On the relevant arc 1 ≤ b ≤ 2 , so it lies in [ 30 , 34 ] .

Mathematics - Circle Question with Solution | TestHub

MathematicsCirclePosition of a point w.r.t a circle, Parametric equation of a circleMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

Given $A = {(x, y) : y \geq 1}, B = {(x, y) : (x - 2)^{2} + y^{2} = 9}$ , and $C = {(x, y) : x + y = 2}$ ,

if $(a, b) \in A \cap B \cap C$ , then $(a + 1)^{2} + (a - 5)^{2} + 2 (b - 1)^{2}$ lies in which interval?

Answer:

Solution:

The expression equals $2 [(a - 2)^{2} + b^{2}] + 20 - 4 b = 38 - 4 b$ . On the relevant arc $1 \leq b \leq 2$ , so it lies in $[30, 34]$ .

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Position of a point w.r.t a circle, Parametric equation of a circle

⏱ 2mℹ️ Source: QB

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