The line $lx + my + n = 0$ will be a tangent to the circle ${x^2} + {y^2} = {a^2}$ if
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
$a(l + m) = n$
Similar Questions
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- [IIT 2019]
Match the statements in Column $I$ with the properties Column $II$ and indicate your answer by darkening the appropriate bubbles in the $4 \times 4$ matrix given in the $ORS$.
Column $I$
Column $II$
$(A)$ Two intersecting circles
$(p)$ have a common tangent
$(B)$ Two mutually external circles
$(q)$ have a common normal
$(C)$ two circles, one strictly inside the other
$(r)$ do not have a common tangent
$(D)$ two branches of a hyperbola
$(s)$ do not have a common normal
Match the statements in Column $I$ with the properties Column $II$ and indicate your answer by darkening the appropriate bubbles in the $4 \times 4$ matrix given in the $ORS$.
| Column $I$ | Column $II$ |
| $(A)$ Two intersecting circles | $(p)$ have a common tangent |
| $(B)$ Two mutually external circles | $(q)$ have a common normal |
| $(C)$ two circles, one strictly inside the other | $(r)$ do not have a common tangent |
| $(D)$ two branches of a hyperbola | $(s)$ do not have a common normal |
- [IIT 2007]
The line $2 x - y +1=0$ is a tangent to the circle at the point $(2,5)$ and the centre of the circle lies on $x-2 y=4$. Then, the radius of the circle is
The line $2 x - y +1=0$ is a tangent to the circle at the point $(2,5)$ and the centre of the circle lies on $x-2 y=4$. Then, the radius of the circle is
- [JEE MAIN 2021]
Line $y = x + a\sqrt 2 $ is a tangent to the circle ${x^2} + {y^2} = {a^2}$ at
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