$l x + m y + n = 0$ is a tangent line to the circle $x^{2} + y^{2} = r^{2}$ if

l^{2} + m^{2} = n^{2} r^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

l^{2} + m^{2} = n^{2} + r^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

n^{2} = r^{2} (l^{2} + m^{2})

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $n^{2} = r^{2} (l^{2} + m^{2})$
line is tangent if $\Rightarrow$ distance of line from center $= r$
$∴ ∣ ∣ ∣ \frac{l (0) + m (0) + n}{\sqrt{l^{2} + m^{2}}} ∣ ∣ ∣ = r$
$\frac{n^{2}}{l^{2} + m^{2}} = r^{2}$
$\Rightarrow n^{2} = r^{2} (l^{2} + m^{2})$

Suggest Corrections

Similar questions

The line $l x + m y + n = 0$ will be a tangent to the circle $x^{2} + y^{2} = a^{2}$ iff

x^{2} + y^{2} = a^{2}

l x + m y + n = 0

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

\frac{a^{2}}{l^{2}} - \frac{b^{2}}{m^{2}} = {(\frac{a^{2} + b^{2}}{n})}^{2}

l x + m y + n = 0

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

\frac{a^{2}}{l^{2}} + \frac{b^{2}}{m^{2}} = \frac{(a^{2} - b^{2})^{2}}{n^{2}}

l x + m y = n

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

\frac{n^{2}}{(a^{2} - b^{2})^{2}} (\frac{a^{2}}{l^{2}} + \frac{b^{2}}{m^{2}}) = k,

7 k =

Join BYJU'S Learning Program