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10-1.Circle and System of Circles
easy
If the line $3x - 4y = \lambda $ touches the circle ${x^2} + {y^2} - 4x - 8y - 5 = 0$, then $\lambda $ is equal to
A
$-35, -15$
B
$-35, 15$
C
$35, 15$
D
$35,-15$
Solution
(b) Accordingly, $\frac{{3(2) – 4(4) – \lambda }}{{\sqrt {{3^2} + {4^2}} }} $
$= \pm \sqrt {{2^2} + {4^2} + 5} $
$ \Rightarrow – 10 – \lambda = \pm 25$
$\Rightarrow \lambda = – 35,\;15$.
Standard 11
Mathematics