If the straight line 4x + 3y + = 0 touches the circle 2( x^2 + y^… - Vidyadip

MCQ

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
$\frac{{5\sqrt 5 }}{4}$
✓
$\frac{{5\sqrt {10} }}{2}$

✓

Answer

Correct option: D.

$\frac{{5\sqrt {10} }}{2}$

d
(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 }} $

$= \frac{{5\sqrt {10} }}{2}$.

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