If the line 3x - 4y = touches the circle x^2 + y^2 - 4x - 8y - 5 … - Vidyadip

MCQ

If the line $3x - 4y = \lambda $ touches the circle ${x^2} + {y^2} - 4x - 8y - 5 = 0$, then $\lambda $ is equal to

A
$-35, -15$
✓
$-35, 15$
C
$35, 15$
D
$35,-15$

✓

Answer

Correct option: B.

$-35, 15$

b
(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$

$\Rightarrow \lambda = - 35,\;15$.

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