Line lx + my + n = 0 will be a tangent to circle {x^2} + {y^2} = {a^2} if

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10-1.Circle and System of Circles

easy

The line $lx + my + n = 0$ will be a tangent to the circle ${x^2} + {y^2} = {a^2}$ if

A

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

B

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

C

$n(l + m)a$

D

$a(l + m) = n$

Solution

(b) Line $y = mx + c$ is tangent, if $c = \pm a\sqrt {1 + {m^2}} $.

Now $lx + my + n = 0$ or $y = – \frac{l}{m}x – \frac{n}{m}$ is tangent, if

$ – \frac{n}{m} = \pm a\sqrt {1 + {{\left( {\frac{l}{m}} \right)}^2}} $ or ${n^2} = {a^2}({m^2} + {l^2})$.

Standard 11

Mathematics

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