If line lx + my + n = 0 be a tangent to circle {(x - h)^2} + {(y - k)^2} = {a^2}, then

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10-1.Circle and System of Circles

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If the line $lx + my + n = 0$ be a tangent to the circle ${(x - h)^2} + {(y - k)^2} = {a^2},$ then

A

$hl + km + n = {a^2}({l^2} + {m^2})$

B

${(hl + km + n)^2} = a({l^2} + {m^2})$

C

${(hl + km + n)^2} = {a^2}({l^2} + {m^2})$

D

None of these

Solution

(c) According to the condition, $a = \frac{{hl + mk + n}}{{\sqrt {{l^2} + {m^2}} }}$

$ \Rightarrow {(hl + km + n)^2} $

$= {a^2}({l^2} + {m^2})$.

Standard 11

Mathematics

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