27123335−2−(λ+4)=0⇒12(−21)−3(−39)−(λ+4)(−15)=0⇒−252+117+15(1+4)=0⇒15λ+177−252=0⇒15λ−75=0⇒λ=59816−μ3335−2−9=0⇒1μ−816−μ00377−9=0⇒7−7(μ−8)=0⇒1−(μ−8)=0⇒μ=9⇒ centre of circle (5,9) radius = length of ⊥ from centre (5,9)=520−27=57
Let the system of equations :
$\begin{aligned}
& 2 x+3 y+5 z=9 \
& 7 x+3 y-2 z=8 \
& 12 x+3 y-(4+\lambda) z=16-\mu
\end{aligned}$
have infinitely many solutions. Then the radius of the circle centred at (λ,μ) and touching the line 4x=3y is
Held on 7 Apr 2025 · Verified 6 Jul 2026.
517
57
7
521
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