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10-1.Circle and System of Circles
easy
If the straight line $4x + 3y + \lambda = 0$ touches the circle $2({x^2} + {y^2}) = 5$, then $\lambda $ is
A
$\frac{{5\sqrt 5 }}{2}$
B
$5\sqrt 2 $
C
$\frac{{5\sqrt 5 }}{4}$
D
$\frac{{5\sqrt {10} }}{2}$
Solution
(d) According to equation,
$\frac{{4(0) + 3(0) + \lambda }}{{\sqrt {{4^2} + {3^2}} }}$
$= \sqrt {\frac{5}{2}}$
$\Rightarrow \lambda = \frac{{5\sqrt 5 }}{{\sqrt 2 }} $
$= \frac{{5\sqrt {10} }}{2}$.
Standard 11
Mathematics