Gujarati
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

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